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",[568,1166,1167],{},"Waagerechte Asymptote"," ",[573,1170,1172,1191],{"className":1171},[576],[573,1173,1175],{"className":1174},[580],[582,1176,1177],{"xmlns":584},[586,1178,1179,1188],{},[589,1180,1181,1184,1186],{},[592,1182,1183],{},"y",[596,1185,608],{},[643,1187,645],{},[675,1189,1190],{"encoding":677},"y = 0",[573,1192,1194,1214],{"className":1193,"ariaHidden":683},[682],[573,1195,1197,1201,1205,1208,1211],{"className":1196},[687],[573,1198],{"className":1199,"style":1200},[691],"height:0.625em;vertical-align:-0.1944em;",[573,1202,1183],{"className":1203,"style":1204},[696,697],"margin-right:0.0359em;",[573,1206],{"className":1207,"style":714},[713],[573,1209,608],{"className":1210},[718],[573,1212],{"className":1213,"style":714},[713],[573,1215,1217,1221],{"className":1216},[687],[573,1218],{"className":1219,"style":1220},[691],"height:0.6444em;",[573,1222,645],{"className":1223},[696],".",[1108,1226,1227,1278,1279,1224],{},[573,1228,1230,1248],{"className":1229},[576],[573,1231,1233],{"className":1232},[580],[582,1234,1235],{"xmlns":584},[586,1236,1237,1245],{},[589,1238,1239,1241,1243],{},[592,1240,622],{},[596,1242,608],{},[592,1244,655],{},[675,1246,1247],{"encoding":677},"n = m",[573,1249,1251,1269],{"className":1250,"ariaHidden":683},[682],[573,1252,1254,1257,1260,1263,1266],{"className":1253},[687],[573,1255],{"className":1256,"style":1160},[691],[573,1258,622],{"className":1259},[696,697],[573,1261],{"className":1262,"style":714},[713],[573,1264,608],{"className":1265},[718],[573,1267],{"className":1268,"style":714},[713],[573,1270,1272,1275],{"className":1271},[687],[573,1273],{"className":1274,"style":1160},[691],[573,1276,655],{"className":1277},[696,697],": Die höchsten Potenzen kürzen sich weg. Waagerechte Asymptote ",[573,1280,1282,1312],{"className":1281},[576],[573,1283,1285],{"className":1284},[580],[582,1286,1287],{"xmlns":584},[586,1288,1289,1309],{},[589,1290,1291,1293,1295],{},[592,1292,1183],{},[596,1294,608],{},[610,1296,1297,1303],{},[615,1298,1299,1301],{},[592,1300,619],{},[592,1302,622],{},[615,1304,1305,1307],{},[592,1306,652],{},[592,1308,655],{},[675,1310,1311],{"encoding":677},"y = \\frac{a_n}{b_m}",[573,1313,1315,1333],{"className":1314,"ariaHidden":683},[682],[573,1316,1318,1321,1324,1327,1330],{"className":1317},[687],[573,1319],{"className":1320,"style":1200},[691],[573,1322,1183],{"className":1323,"style":1204},[696,697],[573,1325],{"className":1326,"style":714},[713],[573,1328,608],{"className":1329},[718],[573,1331],{"className":1332,"style":714},[713],[573,1334,1336,1340],{"className":1335},[687],[573,1337],{"className":1338,"style":1339},[691],"height:1.1566em;vertical-align:-0.4451em;",[573,1341,1343,1346,1480],{"className":1342},[696],[573,1344],{"className":1345},[702,735],[573,1347,1349],{"className":1348},[610],[573,1350,1352,1472],{"className":1351},[742,743],[573,1353,1355,1469],{"className":1354},[747],[573,1356,1359,1410,1418],{"className":1357,"style":1358},[751],"height:0.7115em;",[573,1360,1361,1364],{"style":755},[573,1362],{"className":1363,"style":760},[759],[573,1365,1367],{"className":1366},[764,765,766,767],[573,1368,1370],{"className":1369},[696,767],[573,1371,1373,1376],{"className":1372},[696,767],[573,1374,652],{"className":1375},[696,697,767],[573,1377,1379],{"className":1378},[780],[573,1380,1382,1402],{"className":1381},[742,743],[573,1383,1385,1399],{"className":1384},[747],[573,1386,1388],{"className":1387,"style":790},[751],[573,1389,1390,1393],{"style":793},[573,1391],{"className":1392,"style":797},[759],[573,1394,1396],{"className":1395},[764,801,802,767],[573,1397,655],{"className":1398},[696,697,767],[573,1400,810],{"className":1401},[809],[573,1403,1405],{"className":1404},[747],[573,1406,1408],{"className":1407,"style":817},[751],[573,1409],{},[573,1411,1412,1415],{"style":905},[573,1413],{"className":1414,"style":760},[759],[573,1416],{"className":1417,"style":913},[912],[573,1419,1420,1423],{"style":916},[573,1421],{"className":1422,"style":760},[759],[573,1424,1426],{"className":1425},[764,765,766,767],[573,1427,1429],{"className":1428},[696,767],[573,1430,1432,1435],{"className":1431},[696,767],[573,1433,619],{"className":1434},[696,697,767],[573,1436,1438],{"className":1437},[780],[573,1439,1441,1461],{"className":1440},[742,743],[573,1442,1444,1458],{"className":1443},[747],[573,1445,1447],{"className":1446,"style":790},[751],[573,1448,1449,1452],{"style":793},[573,1450],{"className":1451,"style":797},[759],[573,1453,1455],{"className":1454},[764,801,802,767],[573,1456,622],{"className":1457},[696,697,767],[573,1459,810],{"className":1460},[809],[573,1462,1464],{"className":1463},[747],[573,1465,1467],{"className":1466,"style":817},[751],[573,1468],{},[573,1470,810],{"className":1471},[809],[573,1473,1475],{"className":1474},[747],[573,1476,1478],{"className":1477,"style":1055},[751],[573,1479],{},[573,1481],{"className":1482},[709,735],[1108,1484,1485,1561,1562,1168,1564,1645,1646,1224],{},[573,1486,1488,1511],{"className":1487},[576],[573,1489,1491],{"className":1490},[580],[582,1492,1493],{"xmlns":584},[586,1494,1495,1508],{},[589,1496,1497,1499,1501,1503,1505],{},[592,1498,622],{},[596,1500,608],{},[592,1502,655],{},[596,1504,632],{},[643,1506,1507],{},"1",[675,1509,1510],{"encoding":677},"n = m + 1",[573,1512,1514,1532,1552],{"className":1513,"ariaHidden":683},[682],[573,1515,1517,1520,1523,1526,1529],{"className":1516},[687],[573,1518],{"className":1519,"style":1160},[691],[573,1521,622],{"className":1522},[696,697],[573,1524],{"className":1525,"style":714},[713],[573,1527,608],{"className":1528},[718],[573,1530],{"className":1531,"style":714},[713],[573,1533,1535,1539,1542,1546,1549],{"className":1534},[687],[573,1536],{"className":1537,"style":1538},[691],"height:0.6667em;vertical-align:-0.0833em;",[573,1540,655],{"className":1541},[696,697],[573,1543],{"className":1544,"style":1545},[713],"margin-right:0.2222em;",[573,1547,632],{"className":1548},[854],[573,1550],{"className":1551,"style":1545},[713],[573,1553,1555,1558],{"className":1554},[687],[573,1556],{"className":1557,"style":1220},[691],[573,1559,1507],{"className":1560},[696],": Es gibt eine ",[568,1563,551],{},[573,1565,1567,1593],{"className":1566},[576],[573,1568,1570],{"className":1569},[580],[582,1571,1572],{"xmlns":584},[586,1573,1574,1590],{},[589,1575,1576,1578,1580,1583,1585,1587],{},[592,1577,1183],{},[596,1579,608],{},[592,1581,1582],{},"s",[592,1584,602],{},[596,1586,632],{},[592,1588,1589],{},"t",[675,1591,1592],{"encoding":677},"y = sx + t",[573,1594,1596,1614,1635],{"className":1595,"ariaHidden":683},[682],[573,1597,1599,1602,1605,1608,1611],{"className":1598},[687],[573,1600],{"className":1601,"style":1200},[691],[573,1603,1183],{"className":1604,"style":1204},[696,697],[573,1606],{"className":1607,"style":714},[713],[573,1609,608],{"className":1610},[718],[573,1612],{"className":1613,"style":714},[713],[573,1615,1617,1620,1623,1626,1629,1632],{"className":1616},[687],[573,1618],{"className":1619,"style":1538},[691],[573,1621,1582],{"className":1622},[696,697],[573,1624,602],{"className":1625},[696,697],[573,1627],{"className":1628,"style":1545},[713],[573,1630,632],{"className":1631},[854],[573,1633],{"className":1634,"style":1545},[713],[573,1636,1638,1642],{"className":1637},[687],[573,1639],{"className":1640,"style":1641},[691],"height:0.6151em;",[573,1643,1589],{"className":1644},[696,697],". Man findet sie mit Polynomdivision: Der ganzrationale Teil des Ergebnisses ist die Asymptote, der Restbruch geht gegen ",[573,1647,1649,1662],{"className":1648},[576],[573,1650,1652],{"className":1651},[580],[582,1653,1654],{"xmlns":584},[586,1655,1656,1660],{},[589,1657,1658],{},[643,1659,645],{},[675,1661,645],{"encoding":677},[573,1663,1665],{"className":1664,"ariaHidden":683},[682],[573,1666,1668,1671],{"className":1667},[687],[573,1669],{"className":1670,"style":1220},[691],[573,1672,645],{"className":1673},[696],[1108,1675,1676,1750],{},[573,1677,1679,1702],{"className":1678},[576],[573,1680,1682],{"className":1681},[580],[582,1683,1684],{"xmlns":584},[586,1685,1686,1699],{},[589,1687,1688,1690,1693,1695,1697],{},[592,1689,622],{},[596,1691,1692],{},">",[592,1694,655],{},[596,1696,632],{},[643,1698,1507],{},[675,1700,1701],{"encoding":677},"n > m + 1",[573,1703,1705,1723,1741],{"className":1704,"ariaHidden":683},[682],[573,1706,1708,1711,1714,1717,1720],{"className":1707},[687],[573,1709],{"className":1710,"style":1141},[691],[573,1712,622],{"className":1713},[696,697],[573,1715],{"className":1716,"style":714},[713],[573,1718,1692],{"className":1719},[718],[573,1721],{"className":1722,"style":714},[713],[573,1724,1726,1729,1732,1735,1738],{"className":1725},[687],[573,1727],{"className":1728,"style":1538},[691],[573,1730,655],{"className":1731},[696,697],[573,1733],{"className":1734,"style":1545},[713],[573,1736,632],{"className":1737},[854],[573,1739],{"className":1740,"style":1545},[713],[573,1742,1744,1747],{"className":1743},[687],[573,1745],{"className":1746,"style":1220},[691],[573,1748,1507],{"className":1749},[696],": Der Graph nähert sich einer ganzrationalen Kurve höheren Grades, es gibt keine Asymptote als Gerade.",[564,1752,1753,1756],{},[568,1754,1755],{},"Senkrechte Asymptoten"," liegen an den Polstellen, also an Nullstellen des Nenners, die sich nicht wegkürzen lassen.",[559,1758,1760],{"id":1759},"beispiele","Beispiele",[564,1762,1763,1996,1997,2025,2026,2171,2172,2229,2230,1224],{},[573,1764,1766,1819],{"className":1765},[576],[573,1767,1769],{"className":1768},[580],[582,1770,1771],{"xmlns":584},[586,1772,1773,1816],{},[589,1774,1775,1777,1779,1781,1783,1785],{},[592,1776,594],{},[596,1778,599],{"stretchy":598},[592,1780,602],{},[596,1782,605],{"stretchy":598},[596,1784,608],{},[610,1786,1787,1802],{},[589,1788,1789,1792,1798,1800],{},[643,1790,1791],{},"2",[624,1793,1794,1796],{},[592,1795,602],{},[643,1797,1791],{},[596,1799,632],{},[643,1801,1507],{},[589,1803,1804,1810,1813],{},[624,1805,1806,1808],{},[592,1807,602],{},[643,1809,1791],{},[596,1811,1812],{},"−",[643,1814,1815],{},"4",[675,1817,1818],{"encoding":677},"f(x) = \\frac{2x^2 + 1}{x^2 - 4}",[573,1820,1822,1849],{"className":1821,"ariaHidden":683},[682],[573,1823,1825,1828,1831,1834,1837,1840,1843,1846],{"className":1824},[687],[573,1826],{"className":1827,"style":692},[691],[573,1829,594],{"className":1830,"style":698},[696,697],[573,1832,599],{"className":1833},[702],[573,1835,602],{"className":1836},[696,697],[573,1838,605],{"className":1839},[709],[573,1841],{"className":1842,"style":714},[713],[573,1844,608],{"className":1845},[718],[573,1847],{"className":1848,"style":714},[713],[573,1850,1852,1856],{"className":1851},[687],[573,1853],{"className":1854,"style":1855},[691],"height:1.4213em;vertical-align:-0.4033em;",[573,1857,1859,1862,1993],{"className":1858},[696],[573,1860],{"className":1861},[702,735],[573,1863,1865],{"className":1864},[610],[573,1866,1868,1984],{"className":1867},[742,743],[573,1869,1871,1981],{"className":1870},[747],[573,1872,1875,1922,1930],{"className":1873,"style":1874},[751],"height:1.0179em;",[573,1876,1877,1880],{"style":755},[573,1878],{"className":1879,"style":760},[759],[573,1881,1883],{"className":1882},[764,765,766,767],[573,1884,1886,1916,1919],{"className":1885},[696,767],[573,1887,1889,1892],{"className":1888},[696,767],[573,1890,602],{"className":1891},[696,697,767],[573,1893,1895],{"className":1894},[780],[573,1896,1898],{"className":1897},[742],[573,1899,1901],{"className":1900},[747],[573,1902,1905],{"className":1903,"style":1904},[751],"height:0.7463em;",[573,1906,1907,1910],{"style":841},[573,1908],{"className":1909,"style":797},[759],[573,1911,1913],{"className":1912},[764,801,802,767],[573,1914,1791],{"className":1915},[696,767],[573,1917,1812],{"className":1918},[854,767],[573,1920,1815],{"className":1921},[696,767],[573,1923,1924,1927],{"style":905},[573,1925],{"className":1926,"style":760},[759],[573,1928],{"className":1929,"style":913},[912],[573,1931,1933,1936],{"style":1932},"top:-3.394em;",[573,1934],{"className":1935,"style":760},[759],[573,1937,1939],{"className":1938},[764,765,766,767],[573,1940,1942,1945,1975,1978],{"className":1941},[696,767],[573,1943,1791],{"className":1944},[696,767],[573,1946,1948,1951],{"className":1947},[696,767],[573,1949,602],{"className":1950},[696,697,767],[573,1952,1954],{"className":1953},[780],[573,1955,1957],{"className":1956},[742],[573,1958,1960],{"className":1959},[747],[573,1961,1964],{"className":1962,"style":1963},[751],"height:0.8913em;",[573,1965,1966,1969],{"style":987},[573,1967],{"className":1968,"style":797},[759],[573,1970,1972],{"className":1971},[764,801,802,767],[573,1973,1791],{"className":1974},[696,767],[573,1976,632],{"className":1977},[854,767],[573,1979,1507],{"className":1980},[696,767],[573,1982,810],{"className":1983},[809],[573,1985,1987],{"className":1986},[747],[573,1988,1991],{"className":1989,"style":1990},[751],"height:0.4033em;",[573,1992],{},[573,1994],{"className":1995},[709,735],": Zähler- und Nennergrad sind ",[573,1998,2000,2013],{"className":1999},[576],[573,2001,2003],{"className":2002},[580],[582,2004,2005],{"xmlns":584},[586,2006,2007,2011],{},[589,2008,2009],{},[643,2010,1791],{},[675,2012,1791],{"encoding":677},[573,2014,2016],{"className":2015,"ariaHidden":683},[682],[573,2017,2019,2022],{"className":2018},[687],[573,2020],{"className":2021,"style":1220},[691],[573,2023,1791],{"className":2024},[696],". Die waagerechte Asymptote ist ",[573,2027,2029,2055],{"className":2028},[576],[573,2030,2032],{"className":2031},[580],[582,2033,2034],{"xmlns":584},[586,2035,2036,2052],{},[589,2037,2038,2040,2042,2048,2050],{},[592,2039,1183],{},[596,2041,608],{},[610,2043,2044,2046],{},[643,2045,1791],{},[643,2047,1507],{},[596,2049,608],{},[643,2051,1791],{},[675,2053,2054],{"encoding":677},"y = \\frac{2}{1} = 2",[573,2056,2058,2076,2162],{"className":2057,"ariaHidden":683},[682],[573,2059,2061,2064,2067,2070,2073],{"className":2060},[687],[573,2062],{"className":2063,"style":1200},[691],[573,2065,1183],{"className":2066,"style":1204},[696,697],[573,2068],{"className":2069,"style":714},[713],[573,2071,608],{"className":2072},[718],[573,2074],{"className":2075,"style":714},[713],[573,2077,2079,2083,2153,2156,2159],{"className":2078},[687],[573,2080],{"className":2081,"style":2082},[691],"height:1.1901em;vertical-align:-0.345em;",[573,2084,2086,2089,2150],{"className":2085},[696],[573,2087],{"className":2088},[702,735],[573,2090,2092],{"className":2091},[610],[573,2093,2095,2141],{"className":2094},[742,743],[573,2096,2098,2138],{"className":2097},[747],[573,2099,2102,2116,2124],{"className":2100,"style":2101},[751],"height:0.8451em;",[573,2103,2104,2107],{"style":755},[573,2105],{"className":2106,"style":760},[759],[573,2108,2110],{"className":2109},[764,765,766,767],[573,2111,2113],{"className":2112},[696,767],[573,2114,1507],{"className":2115},[696,767],[573,2117,2118,2121],{"style":905},[573,2119],{"className":2120,"style":760},[759],[573,2122],{"className":2123,"style":913},[912],[573,2125,2126,2129],{"style":1932},[573,2127],{"className":2128,"style":760},[759],[573,2130,2132],{"className":2131},[764,765,766,767],[573,2133,2135],{"className":2134},[696,767],[573,2136,1791],{"className":2137},[696,767],[573,2139,810],{"className":2140},[809],[573,2142,2144],{"className":2143},[747],[573,2145,2148],{"className":2146,"style":2147},[751],"height:0.345em;",[573,2149],{},[573,2151],{"className":2152},[709,735],[573,2154],{"className":2155,"style":714},[713],[573,2157,608],{"className":2158},[718],[573,2160],{"className":2161,"style":714},[713],[573,2163,2165,2168],{"className":2164},[687],[573,2166],{"className":2167,"style":1220},[691],[573,2169,1791],{"className":2170},[696],". Senkrechte Asymptoten liegen bei ",[573,2173,2175,2195],{"className":2174},[576],[573,2176,2178],{"className":2177},[580],[582,2179,2180],{"xmlns":584},[586,2181,2182,2192],{},[589,2183,2184,2186,2188,2190],{},[592,2185,602],{},[596,2187,608],{},[596,2189,1812],{},[643,2191,1791],{},[675,2193,2194],{"encoding":677},"x = -2",[573,2196,2198,2216],{"className":2197,"ariaHidden":683},[682],[573,2199,2201,2204,2207,2210,2213],{"className":2200},[687],[573,2202],{"className":2203,"style":1160},[691],[573,2205,602],{"className":2206},[696,697],[573,2208],{"className":2209,"style":714},[713],[573,2211,608],{"className":2212},[718],[573,2214],{"className":2215,"style":714},[713],[573,2217,2219,2223,2226],{"className":2218},[687],[573,2220],{"className":2221,"style":2222},[691],"height:0.7278em;vertical-align:-0.0833em;",[573,2224,1812],{"className":2225},[696],[573,2227,1791],{"className":2228},[696]," und ",[573,2231,2233,2251],{"className":2232},[576],[573,2234,2236],{"className":2235},[580],[582,2237,2238],{"xmlns":584},[586,2239,2240,2248],{},[589,2241,2242,2244,2246],{},[592,2243,602],{},[596,2245,608],{},[643,2247,1791],{},[675,2249,2250],{"encoding":677},"x = 2",[573,2252,2254,2272],{"className":2253,"ariaHidden":683},[682],[573,2255,2257,2260,2263,2266,2269],{"className":2256},[687],[573,2258],{"className":2259,"style":1160},[691],[573,2261,602],{"className":2262},[696,697],[573,2264],{"className":2265,"style":714},[713],[573,2267,608],{"className":2268},[718],[573,2270],{"className":2271,"style":714},[713],[573,2273,2275,2278],{"className":2274},[687],[573,2276],{"className":2277,"style":1220},[691],[573,2279,1791],{"className":2280},[696],[564,2282,2283,2472,2473,2501],{},[573,2284,2286,2330],{"className":2285},[576],[573,2287,2289],{"className":2288},[580],[582,2290,2291],{"xmlns":584},[586,2292,2293,2327],{},[589,2294,2295,2297,2299,2301,2303,2305],{},[592,2296,594],{},[596,2298,599],{"stretchy":598},[592,2300,602],{},[596,2302,605],{"stretchy":598},[596,2304,608],{},[610,2306,2307,2319],{},[589,2308,2309,2315,2317],{},[624,2310,2311,2313],{},[592,2312,602],{},[643,2314,1791],{},[596,2316,632],{},[643,2318,1507],{},[589,2320,2321,2323,2325],{},[592,2322,602],{},[596,2324,1812],{},[643,2326,1507],{},[675,2328,2329],{"encoding":677},"f(x) = \\frac{x^2 + 1}{x - 1}",[573,2331,2333,2360],{"className":2332,"ariaHidden":683},[682],[573,2334,2336,2339,2342,2345,2348,2351,2354,2357],{"className":2335},[687],[573,2337],{"className":2338,"style":692},[691],[573,2340,594],{"className":2341,"style":698},[696,697],[573,2343,599],{"className":2344},[702],[573,2346,602],{"className":2347},[696,697],[573,2349,605],{"className":2350},[709],[573,2352],{"className":2353,"style":714},[713],[573,2355,608],{"className":2356},[718],[573,2358],{"className":2359,"style":714},[713],[573,2361,2363,2366],{"className":2362},[687],[573,2364],{"className":2365,"style":1855},[691],[573,2367,2369,2372,2469],{"className":2368},[696],[573,2370],{"className":2371},[702,735],[573,2373,2375],{"className":2374},[610],[573,2376,2378,2461],{"className":2377},[742,743],[573,2379,2381,2458],{"className":2380},[747],[573,2382,2384,2404,2412],{"className":2383,"style":1874},[751],[573,2385,2386,2389],{"style":755},[573,2387],{"className":2388,"style":760},[759],[573,2390,2392],{"className":2391},[764,765,766,767],[573,2393,2395,2398,2401],{"className":2394},[696,767],[573,2396,602],{"className":2397},[696,697,767],[573,2399,1812],{"className":2400},[854,767],[573,2402,1507],{"className":2403},[696,767],[573,2405,2406,2409],{"style":905},[573,2407],{"className":2408,"style":760},[759],[573,2410],{"className":2411,"style":913},[912],[573,2413,2414,2417],{"style":1932},[573,2415],{"className":2416,"style":760},[759],[573,2418,2420],{"className":2419},[764,765,766,767],[573,2421,2423,2452,2455],{"className":2422},[696,767],[573,2424,2426,2429],{"className":2425},[696,767],[573,2427,602],{"className":2428},[696,697,767],[573,2430,2432],{"className":2431},[780],[573,2433,2435],{"className":2434},[742],[573,2436,2438],{"className":2437},[747],[573,2439,2441],{"className":2440,"style":1963},[751],[573,2442,2443,2446],{"style":987},[573,2444],{"className":2445,"style":797},[759],[573,2447,2449],{"className":2448},[764,801,802,767],[573,2450,1791],{"className":2451},[696,767],[573,2453,632],{"className":2454},[854,767],[573,2456,1507],{"className":2457},[696,767],[573,2459,810],{"className":2460},[809],[573,2462,2464],{"className":2463},[747],[573,2465,2467],{"className":2466,"style":1990},[751],[573,2468],{},[573,2470],{"className":2471},[709,735],": Der Zählergrad ist um ",[573,2474,2476,2489],{"className":2475},[576],[573,2477,2479],{"className":2478},[580],[582,2480,2481],{"xmlns":584},[586,2482,2483,2487],{},[589,2484,2485],{},[643,2486,1507],{},[675,2488,1507],{"encoding":677},[573,2490,2492],{"className":2491,"ariaHidden":683},[682],[573,2493,2495,2498],{"className":2494},[687],[573,2496],{"className":2497,"style":1220},[691],[573,2499,1507],{"className":2500},[696]," größer. Polynomdivision ergibt",[573,2503,2506],{"className":2504},[2505],"katex-display",[573,2507,2509,2566],{"className":2508},[576],[573,2510,2512],{"className":2511},[580],[582,2513,2515],{"xmlns":584,"display":2514},"block",[586,2516,2517,2563],{},[589,2518,2519,2541,2543,2545,2547,2549,2551],{},[610,2520,2521,2533],{},[589,2522,2523,2529,2531],{},[624,2524,2525,2527],{},[592,2526,602],{},[643,2528,1791],{},[596,2530,632],{},[643,2532,1507],{},[589,2534,2535,2537,2539],{},[592,2536,602],{},[596,2538,1812],{},[643,2540,1507],{},[596,2542,608],{},[592,2544,602],{},[596,2546,632],{},[643,2548,1507],{},[596,2550,632],{},[610,2552,2553,2555],{},[643,2554,1791],{},[589,2556,2557,2559,2561],{},[592,2558,602],{},[596,2560,1812],{},[643,2562,1507],{},[675,2564,2565],{"encoding":677},"\\frac{x^2 + 1}{x - 1} = x + 1 + \\frac{2}{x - 1}",[573,2567,2569,2704,2722,2740],{"className":2568,"ariaHidden":683},[682],[573,2570,2572,2576,2695,2698,2701],{"className":2571},[687],[573,2573],{"className":2574,"style":2575},[691],"height:2.2604em;vertical-align:-0.7693em;",[573,2577,2579,2582,2692],{"className":2578},[696],[573,2580],{"className":2581},[702,735],[573,2583,2585],{"className":2584},[610],[573,2586,2588,2683],{"className":2587},[742,743],[573,2589,2591,2680],{"className":2590},[747],[573,2592,2595,2619,2627],{"className":2593,"style":2594},[751],"height:1.4911em;",[573,2596,2598,2601],{"style":2597},"top:-2.314em;",[573,2599],{"className":2600,"style":760},[759],[573,2602,2604,2607,2610,2613,2616],{"className":2603},[696],[573,2605,602],{"className":2606},[696,697],[573,2608],{"className":2609,"style":1545},[713],[573,2611,1812],{"className":2612},[854],[573,2614],{"className":2615,"style":1545},[713],[573,2617,1507],{"className":2618},[696],[573,2620,2621,2624],{"style":905},[573,2622],{"className":2623,"style":760},[759],[573,2625],{"className":2626,"style":913},[912],[573,2628,2630,2633],{"style":2629},"top:-3.677em;",[573,2631],{"className":2632,"style":760},[759],[573,2634,2636,2668,2671,2674,2677],{"className":2635},[696],[573,2637,2639,2642],{"className":2638},[696],[573,2640,602],{"className":2641},[696,697],[573,2643,2645],{"className":2644},[780],[573,2646,2648],{"className":2647},[742],[573,2649,2651],{"className":2650},[747],[573,2652,2655],{"className":2653,"style":2654},[751],"height:0.8141em;",[573,2656,2658,2662],{"style":2657},"top:-3.063em;margin-right:0.05em;",[573,2659],{"className":2660,"style":2661},[759],"height:2.7em;",[573,2663,2665],{"className":2664},[764,765,766,767],[573,2666,1791],{"className":2667},[696,767],[573,2669],{"className":2670,"style":1545},[713],[573,2672,632],{"className":2673},[854],[573,2675],{"className":2676,"style":1545},[713],[573,2678,1507],{"className":2679},[696],[573,2681,810],{"className":2682},[809],[573,2684,2686],{"className":2685},[747],[573,2687,2690],{"className":2688,"style":2689},[751],"height:0.7693em;",[573,2691],{},[573,2693],{"className":2694},[709,735],[573,2696],{"className":2697,"style":714},[713],[573,2699,608],{"className":2700},[718],[573,2702],{"className":2703,"style":714},[713],[573,2705,2707,2710,2713,2716,2719],{"className":2706},[687],[573,2708],{"className":2709,"style":1538},[691],[573,2711,602],{"className":2712},[696,697],[573,2714],{"className":2715,"style":1545},[713],[573,2717,632],{"className":2718},[854],[573,2720],{"className":2721,"style":1545},[713],[573,2723,2725,2728,2731,2734,2737],{"className":2724},[687],[573,2726],{"className":2727,"style":2222},[691],[573,2729,1507],{"className":2730},[696],[573,2732],{"className":2733,"style":1545},[713],[573,2735,632],{"className":2736},[854],[573,2738],{"className":2739,"style":1545},[713],[573,2741,2743,2747],{"className":2742},[687],[573,2744],{"className":2745,"style":2746},[691],"height:2.0908em;vertical-align:-0.7693em;",[573,2748,2750,2753,2819],{"className":2749},[696],[573,2751],{"className":2752},[702,735],[573,2754,2756],{"className":2755},[610],[573,2757,2759,2811],{"className":2758},[742,743],[573,2760,2762,2808],{"className":2761},[747],[573,2763,2766,2789,2797],{"className":2764,"style":2765},[751],"height:1.3214em;",[573,2767,2768,2771],{"style":2597},[573,2769],{"className":2770,"style":760},[759],[573,2772,2774,2777,2780,2783,2786],{"className":2773},[696],[573,2775,602],{"className":2776},[696,697],[573,2778],{"className":2779,"style":1545},[713],[573,2781,1812],{"className":2782},[854],[573,2784],{"className":2785,"style":1545},[713],[573,2787,1507],{"className":2788},[696],[573,2790,2791,2794],{"style":905},[573,2792],{"className":2793,"style":760},[759],[573,2795],{"className":2796,"style":913},[912],[573,2798,2799,2802],{"style":2629},[573,2800],{"className":2801,"style":760},[759],[573,2803,2805],{"className":2804},[696],[573,2806,1791],{"className":2807},[696],[573,2809,810],{"className":2810},[809],[573,2812,2814],{"className":2813},[747],[573,2815,2817],{"className":2816,"style":2689},[751],[573,2818],{},[573,2820],{"className":2821},[709,735],[564,2823,2824,2825,2853,2854,1224],{},"Der Restbruch geht gegen ",[573,2826,2828,2841],{"className":2827},[576],[573,2829,2831],{"className":2830},[580],[582,2832,2833],{"xmlns":584},[586,2834,2835,2839],{},[589,2836,2837],{},[643,2838,645],{},[675,2840,645],{"encoding":677},[573,2842,2844],{"className":2843,"ariaHidden":683},[682],[573,2845,2847,2850],{"className":2846},[687],[573,2848],{"className":2849,"style":1220},[691],[573,2851,645],{"className":2852},[696],", die schiefe Asymptote ist ",[573,2855,2857,2879],{"className":2856},[576],[573,2858,2860],{"className":2859},[580],[582,2861,2862],{"xmlns":584},[586,2863,2864,2876],{},[589,2865,2866,2868,2870,2872,2874],{},[592,2867,1183],{},[596,2869,608],{},[592,2871,602],{},[596,2873,632],{},[643,2875,1507],{},[675,2877,2878],{"encoding":677},"y = x + 1",[573,2880,2882,2900,2918],{"className":2881,"ariaHidden":683},[682],[573,2883,2885,2888,2891,2894,2897],{"className":2884},[687],[573,2886],{"className":2887,"style":1200},[691],[573,2889,1183],{"className":2890,"style":1204},[696,697],[573,2892],{"className":2893,"style":714},[713],[573,2895,608],{"className":2896},[718],[573,2898],{"className":2899,"style":714},[713],[573,2901,2903,2906,2909,2912,2915],{"className":2902},[687],[573,2904],{"className":2905,"style":1538},[691],[573,2907,602],{"className":2908},[696,697],[573,2910],{"className":2911,"style":1545},[713],[573,2913,632],{"className":2914},[854],[573,2916],{"className":2917,"style":1545},[713],[573,2919,2921,2924],{"className":2920},[687],[573,2922],{"className":2923,"style":1220},[691],[573,2925,1507],{"className":2926},[696],[564,2928,2929,3115,3116,1224],{},[573,2930,2932,2975],{"className":2931},[576],[573,2933,2935],{"className":2934},[580],[582,2936,2937],{"xmlns":584},[586,2938,2939,2972],{},[589,2940,2941,2943,2945,2947,2949,2951],{},[592,2942,594],{},[596,2944,599],{"stretchy":598},[592,2946,602],{},[596,2948,605],{"stretchy":598},[596,2950,608],{},[610,2952,2953,2960],{},[589,2954,2955,2958],{},[643,2956,2957],{},"3",[592,2959,602],{},[589,2961,2962,2968,2970],{},[624,2963,2964,2966],{},[592,2965,602],{},[643,2967,1791],{},[596,2969,632],{},[643,2971,1507],{},[675,2973,2974],{"encoding":677},"f(x) = \\frac{3x}{x^2 + 1}",[573,2976,2978,3005],{"className":2977,"ariaHidden":683},[682],[573,2979,2981,2984,2987,2990,2993,2996,2999,3002],{"className":2980},[687],[573,2982],{"className":2983,"style":692},[691],[573,2985,594],{"className":2986,"style":698},[696,697],[573,2988,599],{"className":2989},[702],[573,2991,602],{"className":2992},[696,697],[573,2994,605],{"className":2995},[709],[573,2997],{"className":2998,"style":714},[713],[573,3000,608],{"className":3001},[718],[573,3003],{"className":3004,"style":714},[713],[573,3006,3008,3012],{"className":3007},[687],[573,3009],{"className":3010,"style":3011},[691],"height:1.2484em;vertical-align:-0.4033em;",[573,3013,3015,3018,3112],{"className":3014},[696],[573,3016],{"className":3017},[702,735],[573,3019,3021],{"className":3020},[610],[573,3022,3024,3104],{"className":3023},[742,743],[573,3025,3027,3101],{"className":3026},[747],[573,3028,3030,3076,3084],{"className":3029,"style":2101},[751],[573,3031,3032,3035],{"style":755},[573,3033],{"className":3034,"style":760},[759],[573,3036,3038],{"className":3037},[764,765,766,767],[573,3039,3041,3070,3073],{"className":3040},[696,767],[573,3042,3044,3047],{"className":3043},[696,767],[573,3045,602],{"className":3046},[696,697,767],[573,3048,3050],{"className":3049},[780],[573,3051,3053],{"className":3052},[742],[573,3054,3056],{"className":3055},[747],[573,3057,3059],{"className":3058,"style":1904},[751],[573,3060,3061,3064],{"style":841},[573,3062],{"className":3063,"style":797},[759],[573,3065,3067],{"className":3066},[764,801,802,767],[573,3068,1791],{"className":3069},[696,767],[573,3071,632],{"className":3072},[854,767],[573,3074,1507],{"className":3075},[696,767],[573,3077,3078,3081],{"style":905},[573,3079],{"className":3080,"style":760},[759],[573,3082],{"className":3083,"style":913},[912],[573,3085,3086,3089],{"style":1932},[573,3087],{"className":3088,"style":760},[759],[573,3090,3092],{"className":3091},[764,765,766,767],[573,3093,3095,3098],{"className":3094},[696,767],[573,3096,2957],{"className":3097},[696,767],[573,3099,602],{"className":3100},[696,697,767],[573,3102,810],{"className":3103},[809],[573,3105,3107],{"className":3106},[747],[573,3108,3110],{"className":3109,"style":1990},[751],[573,3111],{},[573,3113],{"className":3114},[709,735],": Der Nennergrad ist größer, die Asymptote ist die x-Achse ",[573,3117,3119,3136],{"className":3118},[576],[573,3120,3122],{"className":3121},[580],[582,3123,3124],{"xmlns":584},[586,3125,3126,3134],{},[589,3127,3128,3130,3132],{},[592,3129,1183],{},[596,3131,608],{},[643,3133,645],{},[675,3135,1190],{"encoding":677},[573,3137,3139,3157],{"className":3138,"ariaHidden":683},[682],[573,3140,3142,3145,3148,3151,3154],{"className":3141},[687],[573,3143],{"className":3144,"style":1200},[691],[573,3146,1183],{"className":3147,"style":1204},[696,697],[573,3149],{"className":3150,"style":714},[713],[573,3152,608],{"className":3153},[718],[573,3155],{"className":3156,"style":714},[713],[573,3158,3160,3163],{"className":3159},[687],[573,3161],{"className":3162,"style":1220},[691],[573,3164,645],{"className":3165},[696],[559,3167,3169],{"id":3168},"typische-fehler","Typische Fehler",[1105,3171,3172,3278,3281,3284],{},[1108,3173,3174,3175,3225,3226,3277],{},"Bei ",[573,3176,3178,3195],{"className":3177},[576],[573,3179,3181],{"className":3180},[580],[582,3182,3183],{"xmlns":584},[586,3184,3185,3193],{},[589,3186,3187,3189,3191],{},[592,3188,622],{},[596,3190,608],{},[592,3192,655],{},[675,3194,1247],{"encoding":677},[573,3196,3198,3216],{"className":3197,"ariaHidden":683},[682],[573,3199,3201,3204,3207,3210,3213],{"className":3200},[687],[573,3202],{"className":3203,"style":1160},[691],[573,3205,622],{"className":3206},[696,697],[573,3208],{"className":3209,"style":714},[713],[573,3211,608],{"className":3212},[718],[573,3214],{"className":3215,"style":714},[713],[573,3217,3219,3222],{"className":3218},[687],[573,3220],{"className":3221,"style":1160},[691],[573,3223,655],{"className":3224},[696,697]," die Asymptote ",[573,3227,3229,3247],{"className":3228},[576],[573,3230,3232],{"className":3231},[580],[582,3233,3234],{"xmlns":584},[586,3235,3236,3244],{},[589,3237,3238,3240,3242],{},[592,3239,1183],{},[596,3241,608],{},[643,3243,1507],{},[675,3245,3246],{"encoding":677},"y = 1",[573,3248,3250,3268],{"className":3249,"ariaHidden":683},[682],[573,3251,3253,3256,3259,3262,3265],{"className":3252},[687],[573,3254],{"className":3255,"style":1200},[691],[573,3257,1183],{"className":3258,"style":1204},[696,697],[573,3260],{"className":3261,"style":714},[713],[573,3263,608],{"className":3264},[718],[573,3266],{"className":3267,"style":714},[713],[573,3269,3271,3274],{"className":3270},[687],[573,3272],{"className":3273,"style":1220},[691],[573,3275,1507],{"className":3276},[696]," angeben. Entscheidend ist der Quotient der Leitkoeffizienten, nicht nur der Grad.",[1108,3279,3280],{},"Bei der schiefen Asymptote den Restbruch mitnehmen. Die Asymptote ist nur der ganzrationale Teil.",[1108,3282,3283],{},"Jede Nennernullstelle als senkrechte Asymptote ansehen. Kürzt sie sich weg, liegt eine hebbare Lücke vor.",[1108,3285,3286,3287,3315,3316,1224],{},"Glauben, der Graph könne seine waagerechte Asymptote nie schneiden. Für endliche ",[573,3288,3290,3303],{"className":3289},[576],[573,3291,3293],{"className":3292},[580],[582,3294,3295],{"xmlns":584},[586,3296,3297,3301],{},[589,3298,3299],{},[592,3300,602],{},[675,3302,602],{"encoding":677},[573,3304,3306],{"className":3305,"ariaHidden":683},[682],[573,3307,3309,3312],{"className":3308},[687],[573,3310],{"className":3311,"style":1160},[691],[573,3313,602],{"className":3314},[696,697]," ist das möglich, die Asymptote beschreibt nur das Verhalten für ",[573,3317,3319,3342],{"className":3318},[576],[573,3320,3322],{"className":3321},[580],[582,3323,3324],{"xmlns":584},[586,3325,3326,3339],{},[589,3327,3328,3330,3333,3336],{},[592,3329,602],{},[596,3331,3332],{},"→",[596,3334,3335],{},"±",[592,3337,3338],{"mathvariant":1076},"∞",[675,3340,3341],{"encoding":677},"x \\to \\pm\\infty",[573,3343,3345,3363],{"className":3344,"ariaHidden":683},[682],[573,3346,3348,3351,3354,3357,3360],{"className":3347},[687],[573,3349],{"className":3350,"style":1160},[691],[573,3352,602],{"className":3353},[696,697],[573,3355],{"className":3356,"style":714},[713],[573,3358,3332],{"className":3359},[718],[573,3361],{"className":3362,"style":714},[713],[573,3364,3366,3369,3372],{"className":3365},[687],[573,3367],{"className":3368,"style":1538},[691],[573,3370,3335],{"className":3371},[696],[573,3373,3338],{"className":3374},[696],{"title":3376,"searchDepth":3377,"depth":3377,"links":3378},"",2,[3379,3380,3381],{"id":561,"depth":3377,"text":562},{"id":1759,"depth":3377,"text":1760},{"id":3168,"depth":3377,"text":3169},[3383,3385,3387,3390,3392],{"lhs":3384,"rhs":1791},"round((2*1000^2 + 1)\u002F(1000^2 - 4), 4)",{"lhs":3386,"rhs":1791},"2\u002F1",{"lhs":3388,"rhs":3389},"(x^2 + 1)\u002F(x - 1)","x + 1 + 2\u002F(x - 1)",{"lhs":3391,"rhs":645},"round((1000^2 + 1)\u002F(1000 - 1) - (1000 + 1), 2)",{"lhs":3393,"rhs":645},"round(3*1000\u002F(1000^2 + 1), 2)","a_n \\neq 0,\\ b_m \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>a\u003C\u002Fmi>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a_n \\neq 0,\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>b\u003C\u002Fmi>\u003Cmi>m\u003C\u002Fmi>\u003C\u002Fmsub>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">b_m \\neq 0\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">b\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.1514em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">m\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md",{"caption":3399,"x":3400,"y":3403,"unit":3406,"ticks":3407,"axes":3408,"items":3409},"Graph von f(x) = (2x² + 1)\u002F(x² − 4): Zähler- und Nennergrad sind gleich, die waagerechte Asymptote ist y = 2; senkrechte Asymptoten bei x = −2 und x = 2",[3401,3402],-6,6,[3404,3405],-4,7,24,[3377,3377],true,[3410,3415,3419,3422,3427,3431,3434,3440],{"type":3411,"from":3412,"to":3413,"style":3414},"segment",[3401,3377],[3402,3377],"dashed",{"type":3411,"from":3416,"to":3418,"style":3414},[3417,3404],-2,[3417,3405],{"type":3411,"from":3420,"to":3421,"style":3414},[3377,3404],[3377,3405],{"type":3423,"expr":3424,"domain":3425},"function","(2*x^2 + 1)\u002F(x^2 - 4)",[3401,3426],-2.01,{"type":3423,"expr":3424,"domain":3428},[3429,3430],-1.99,1.99,{"type":3423,"expr":3424,"domain":3432},[3433,3402],2.01,{"type":3435,"at":3436,"text":3439},"label",[3437,3438],4.4,1.45,"y = 2",{"type":3435,"at":3441,"text":594},[3442,3443],3.6,5.5,"\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" viewBox=\"0 0 288 264\" width=\"288\" height=\"264\" role=\"img\" aria-label=\"Graph von f(x) = (2x² + 1)\u002F(x² − 4): Zähler- und Nennergrad sind gleich, die waagerechte Asymptote ist y = 2; senkrechte Asymptoten bei x = −2 und x = 2\" class=\"formula-figure-svg\">\u003Cdefs>\u003Cmarker id=\"fig-rational-function-asymptotes-arrow\" viewBox=\"0 0 10 10\" refX=\"9\" refY=\"5\" markerWidth=\"7\" markerHeight=\"7\" orient=\"auto-start-reverse\">\u003Cpath d=\"M 0 0 L 10 5 L 0 10 z\" class=\"fig-arrowhead\"\u002F>\u003C\u002Fmarker>\u003CclipPath id=\"fig-rational-function-asymptotes-clip\">\u003Crect x=\"0\" y=\"0\" width=\"288\" height=\"264\"\u002F>\u003C\u002FclipPath>\u003C\u002Fdefs>\u003Cline x1=\"0\" y1=\"168\" x2=\"288\" y2=\"168\" class=\"fig-axis\" marker-end=\"url(#fig-rational-function-asymptotes-arrow)\"\u002F>\u003Cline x1=\"144\" y1=\"264\" x2=\"144\" y2=\"0\" class=\"fig-axis\" marker-end=\"url(#fig-rational-function-asymptotes-arrow)\"\u002F>\u003Cline x1=\"0\" y1=\"165\" x2=\"0\" y2=\"171\" class=\"fig-axis\"\u002F>\u003Ctext x=\"3\" y=\"182\" text-anchor=\"start\" class=\"fig-tick\">−6\u003C\u002Ftext>\u003Cline x1=\"48\" y1=\"165\" x2=\"48\" y2=\"171\" class=\"fig-axis\"\u002F>\u003Ctext x=\"51\" y=\"182\" text-anchor=\"start\" class=\"fig-tick\">−4\u003C\u002Ftext>\u003Cline x1=\"96\" y1=\"165\" x2=\"96\" y2=\"171\" class=\"fig-axis\"\u002F>\u003Ctext x=\"99\" y=\"182\" text-anchor=\"start\" class=\"fig-tick\">−2\u003C\u002Ftext>\u003Cline x1=\"192\" y1=\"165\" x2=\"192\" y2=\"171\" class=\"fig-axis\"\u002F>\u003Ctext x=\"195\" y=\"182\" text-anchor=\"start\" 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