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2}\n\\end{aligned}",[583,1334,1336],{"className":1335,"ariaHidden":634},[633],[583,1337,1339,1343],{"className":1338},[638],[583,1340],{"className":1341,"style":1342},[642],"height:4.9234em;vertical-align:-2.2117em;",[583,1344,1346],{"className":1345},[651],[583,1347,1349,1406],{"className":1348},[1174],[583,1350,1353],{"className":1351},[1352],"col-align-r",[583,1354,1356,1397],{"className":1355},[684,685],[583,1357,1359,1394],{"className":1358},[689],[583,1360,1363,1385],{"className":1361,"style":1362},[693],"height:2.7117em;",[583,1364,1366,1370],{"style":1365},"top:-4.7117em;",[583,1367],{"className":1368,"style":1369},[701],"height:3.4911em;",[583,1371,1373,1376,1379,1382],{"className":1372},[651],[583,1374,1129],{"className":1375,"style":1145},[651,652],[583,1377,605],{"className":1378},[647],[583,1380,609],{"className":1381},[651,652],[583,1383,624],{"className":1384},[730],[583,1386,1388,1391],{"style":1387},"top:-2.2154em;",[583,1389],{"className":1390,"style":1369},[701],[583,1392],{"className":1393},[651],[583,1395,717],{"className":1396},[716],[583,1398,1400],{"className":1399},[689],[583,1401,1404],{"className":1402,"style":1403},[693],"height:2.2117em;",[583,1405],{},[583,1407,1410],{"className":1408},[1409],"col-align-l",[583,1411,1413,1866],{"className":1412},[684,685],[583,1414,1416,1863],{"className":1415},[689],[583,1417,1419,1605],{"className":1418,"style":1362},[693],[583,1420,1421,1424],{"style":1365},[583,1422],{"className":1423,"style":1369},[701],[583,1425,1427,1430,1433,1436,1439],{"className":1426},[651],[583,1428],{"className":1429},[651],[583,1431],{"className":1432,"style":773},[656],[583,1434,971],{"className":1435},[777],[583,1437],{"className":1438,"style":773},[656],[583,1440,1442,1446,1602],{"className":1441},[651],[583,1443],{"className":1444},[647,1445],"nulldelimiter",[583,1447,1449],{"className":1448},[1209],[583,1450,1452,1593],{"className":1451},[684,685],[583,1453,1455,1590],{"className":1454},[689],[583,1456,1459,1527,1538],{"className":1457,"style":1458},[693],"height:1.4911em;",[583,1460,1462,1466],{"style":1461},"top:-2.314em;",[583,1463],{"className":1464,"style":1465},[701],"height:3em;",[583,1467,1469,1500,1503,1506,1509,1512,1515,1518,1521,1524],{"className":1468},[651],[583,1470,1472,1475],{"className":1471},[651],[583,1473,609],{"className":1474},[651,652],[583,1476,1478],{"className":1477},[680],[583,1479,1481],{"className":1480},[684],[583,1482,1484],{"className":1483},[689],[583,1485,1488],{"className":1486,"style":1487},[693],"height:0.7401em;",[583,1489,1491,1494],{"style":1490},"top:-2.989em;margin-right:0.05em;",[583,1492],{"className":1493,"style":702},[701],[583,1495,1497],{"className":1496},[706,707,708,709],[583,1498,1220],{"className":1499},[651,709],[583,1501],{"className":1502,"style":657},[656],[583,1504,612],{"className":1505},[661],[583,1507],{"className":1508,"style":657},[656],[583,1510,1238],{"className":1511},[651],[583,1513,609],{"className":1514},[651,652],[583,1516],{"className":1517,"style":657},[656],[583,1519,1243],{"className":1520},[661],[583,1522],{"className":1523,"style":657},[656],[583,1525,1220],{"className":1526},[651],[583,1528,1530,1533],{"style":1529},"top:-3.23em;",[583,1531],{"className":1532,"style":1465},[701],[583,1534],{"className":1535,"style":1537},[1536],"frac-line","border-bottom-width:0.04em;",[583,1539,1541,1544],{"style":1540},"top:-3.677em;",[583,1542],{"className":1543,"style":1465},[701],[583,1545,1547,1578,1581,1584,1587],{"className":1546},[651],[583,1548,1550,1553],{"className":1549},[651],[583,1551,609],{"className":1552},[651,652],[583,1554,1556],{"className":1555},[680],[583,1557,1559],{"className":1558},[684],[583,1560,1562],{"className":1561},[689],[583,1563,1566],{"className":1564,"style":1565},[693],"height:0.8141em;",[583,1567,1569,1572],{"style":1568},"top:-3.063em;margin-right:0.05em;",[583,1570],{"className":1571,"style":702},[701],[583,1573,1575],{"className":1574},[706,707,708,709],[583,1576,1220],{"className":1577},[651,709],[583,1579],{"className":1580,"style":657},[656],[583,1582,612],{"className":1583},[661],[583,1585],{"className":1586,"style":657},[656],[583,1588,1225],{"className":1589},[651],[583,1591,717],{"className":1592},[716],[583,1594,1596],{"className":1595},[689],[583,1597,1600],{"className":1598,"style":1599},[693],"height:0.7693em;",[583,1601],{},[583,1603],{"className":1604},[730,1445],[583,1606,1607,1610],{"style":1387},[583,1608],{"className":1609,"style":1369},[701],[583,1611,1613,1616,1619,1622,1625,1767,1770,1773,1776],{"className":1612},[651],[583,1614],{"className":1615},[651],[583,1617],{"className":1618,"style":773},[656],[583,1620,971],{"className":1621},[777],[583,1623],{"className":1624,"style":773},[656],[583,1626,1628,1631,1764],{"className":1627},[651],[583,1629],{"className":1630},[647,1445],[583,1632,1634],{"className":1633},[1209],[583,1635,1637,1755],{"className":1636},[684,685],[583,1638,1640,1752],{"className":1639},[689],[583,1641,1644,1694,1702],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kürzt sich weg: hebbare Lücke. Der Graph hat ein Loch bei ",[583,2037,2039,2102],{"className":2038},[586],[583,2040,2042],{"className":2041},[590],[592,2043,2044],{"xmlns":594},[596,2045,2046,2099],{},[599,2047,2048,2084,2086,2088,2090,2093,2095,2097],{},[599,2049,2050,2052,2054,2058,2062,2064,2082],{},[602,2051,605],{"fence":634},[619,2053,1225],{},[2055,2056,2057],"mtext",{}," ",[602,2059,2061],{"fence":634,"lspace":2060,"rspace":2060},"0.05em","|",[2055,2063,2057],{},[1209,2065,2066,2074],{},[599,2067,2068,2070,2072],{},[619,2069,1225],{},[602,2071,1243],{},[619,2073,1225],{},[599,2075,2076,2078,2080],{},[619,2077,1225],{},[602,2079,612],{},[619,2081,1220],{},[602,2083,624],{"fence":634},[602,2085,971],{},[602,2087,605],{"stretchy":604},[619,2089,1225],{},[602,2091,2092],{},"∣",[602,2094,612],{},[619,2096,1220],{},[602,2098,624],{"stretchy":604},[626,2100,2101],{"encoding":628},"\\left(1 \\,\\middle|\\, \\frac{1 + 1}{1 - 2}\\right) = (1 \\mid 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bleibt im Nenner, einfach: Polstelle mit Vorzeichenwechsel. Links davon ist ",[583,2374,2376,2389],{"className":2375},[586],[583,2377,2379],{"className":2378},[590],[592,2380,2381],{"xmlns":594},[596,2382,2383,2387],{},[599,2384,2385],{},[607,2386,1129],{},[626,2388,1129],{"encoding":628},[583,2390,2392],{"className":2391,"ariaHidden":634},[633],[583,2393,2395,2398],{"className":2394},[638],[583,2396],{"className":2397,"style":1141},[642],[583,2399,1129],{"className":2400,"style":1145},[651,652]," negativ, rechts positiv.",[564,2403,2404,2599,2600,2651,2652,1054],{},[583,2405,2407,2450],{"className":2406},[586],[583,2408,2410],{"className":2409},[590],[592,2411,2412],{"xmlns":594},[596,2413,2414,2447],{},[599,2415,2416,2419,2421,2423,2425,2427],{},[607,2417,2418],{},"g",[602,2420,605],{"stretchy":604},[607,2422,609],{},[602,2424,624],{"stretchy":604},[602,2426,971],{},[1209,2428,2429,2431],{},[619,2430,1225],{},[599,2432,2433,2435,2437,2439,2441],{},[602,2434,605],{"stretchy":604},[607,2436,609],{},[602,2438,612],{},[619,2440,1238],{},[1214,2442,2443,2445],{},[602,2444,624],{"stretchy":604},[619,2446,1220],{},[626,2448,2449],{"encoding":628},"g(x) = \\frac{1}{(x - 3)^2}",[583,2451,2453,2481],{"className":2452,"ariaHidden":634},[633],[583,2454,2456,2459,2463,2466,2469,2472,2475,2478],{"className":2455},[638],[583,2457],{"className":2458,"style":643},[642],[583,2460,2418],{"className":2461,"style":2462},[651,652],"margin-right:0.0359em;",[583,2464,605],{"className":2465},[647],[583,2467,609],{"className":2468},[651,652],[583,2470,624],{"className":2471},[730],[583,2473],{"className":2474,"style":773},[656],[583,2476,971],{"className":2477},[777],[583,2479],{"className":2480,"style":773},[656],[583,2482,2484,2488],{"className":2483},[638],[583,2485],{"className":2486,"style":2487},[642],"height:1.3651em;vertical-align:-0.52em;",[583,2489,2491,2494,2596],{"className":2490},[651],[583,2492],{"className":2493},[647,1445],[583,2495,2497],{"className":2496},[1209],[583,2498,2500,2587],{"className":2499},[684,685],[583,2501,2503,2584],{"className":2502},[689],[583,2504,2506,2562,2570],{"className":2505,"style":2203},[693],[583,2507,2508,2511],{"style":2206},[583,2509],{"className":2510,"style":1465},[701],[583,2512,2514],{"className":2513},[706,707,708,709],[583,2515,2517,2520,2523,2526,2529],{"className":2516},[651,709],[583,2518,605],{"className":2519},[647,709],[583,2521,609],{"className":2522},[651,652,709],[583,2524,612],{"className":2525},[661,709],[583,2527,1238],{"className":2528},[651,709],[583,2530,2532,2535],{"className":2531},[730,709],[583,2533,624],{"className":2534},[730,709],[583,2536,2538],{"className":2537},[680],[583,2539,2541],{"className":2540},[684],[583,2542,2544],{"className":2543},[689],[583,2545,2548],{"className":2546,"style":2547},[693],"height:0.7463em;",[583,2549,2551,2555],{"style":2550},"top:-2.786em;margin-right:0.0714em;",[583,2552],{"className":2553,"style":2554},[701],"height:2.5em;",[583,2556,2559],{"className":2557},[706,2558,2125,709],"reset-size3",[583,2560,1220],{"className":2561},[651,709],[583,2563,2564,2567],{"style":1529},[583,2565],{"className":2566,"style":1465},[701],[583,2568],{"className":2569,"style":1537},[1536],[583,2571,2572,2575],{"style":2235},[583,2573],{"className":2574,"style":1465},[701],[583,2576,2578],{"className":2577},[706,707,708,709],[583,2579,2581],{"className":2580},[651,709],[583,2582,1225],{"className":2583},[651,709],[583,2585,717],{"className":2586},[716],[583,2588,2590],{"className":2589},[689],[583,2591,2594],{"className":2592,"style":2593},[693],"height:0.52em;",[583,2595],{},[583,2597],{"className":2598},[730,1445]," hat bei ",[583,2601,2603,2621],{"className":2602},[586],[583,2604,2606],{"className":2605},[590],[592,2607,2608],{"xmlns":594},[596,2609,2610,2618],{},[599,2611,2612,2614,2616],{},[607,2613,609],{},[602,2615,971],{},[619,2617,1238],{},[626,2619,2620],{"encoding":628},"x = 3",[583,2622,2624,2642],{"className":2623,"ariaHidden":634},[633],[583,2625,2627,2630,2633,2636,2639],{"className":2626},[638],[583,2628],{"className":2629,"style":990},[642],[583,2631,609],{"className":2632},[651,652],[583,2634],{"className":2635,"style":773},[656],[583,2637,971],{"className":2638},[777],[583,2640],{"className":2641,"style":773},[656],[583,2643,2645,2648],{"className":2644},[638],[583,2646],{"className":2647,"style":1925},[642],[583,2649,1238],{"className":2650},[651]," eine Polstelle zweiter Ordnung ohne Vorzeichenwechsel: Der Graph geht auf beiden Seiten nach ",[583,2653,2655,2673],{"className":2654},[586],[583,2656,2658],{"className":2657},[590],[592,2659,2660],{"xmlns":594},[596,2661,2662,2670],{},[599,2663,2664,2666],{},[602,2665,1243],{},[607,2667,2669],{"mathvariant":2668},"normal","∞",[626,2671,2672],{"encoding":628},"+\\infty",[583,2674,2676],{"className":2675,"ariaHidden":634},[633],[583,2677,2679,2683,2686],{"className":2678},[638],[583,2680],{"className":2681,"style":2682},[642],"height:0.6667em;vertical-align:-0.0833em;",[583,2684,1243],{"className":2685},[651],[583,2687,2669],{"className":2688},[651],[559,2690,2692],{"id":2691},"typische-fehler","Typische Fehler",[573,2694,2695,2870,2873],{},[576,2696,2697,2698,2726,2727,2777,2778,1054],{},"Vor dem Kürzen die Definitionsmenge vergessen. Auch nach dem Kürzen ist ",[583,2699,2701,2714],{"className":2700},[586],[583,2702,2704],{"className":2703},[590],[592,2705,2706],{"xmlns":594},[596,2707,2708,2712],{},[599,2709,2710],{},[607,2711,1129],{},[626,2713,1129],{"encoding":628},[583,2715,2717],{"className":2716,"ariaHidden":634},[633],[583,2718,2720,2723],{"className":2719},[638],[583,2721],{"className":2722,"style":1141},[642],[583,2724,1129],{"className":2725,"style":1145},[651,652]," bei ",[583,2728,2730,2747],{"className":2729},[586],[583,2731,2733],{"className":2732},[590],[592,2734,2735],{"xmlns":594},[596,2736,2737,2745],{},[599,2738,2739,2741,2743],{},[607,2740,609],{},[602,2742,971],{},[619,2744,1225],{},[626,2746,1897],{"encoding":628},[583,2748,2750,2768],{"className":2749,"ariaHidden":634},[633],[583,2751,2753,2756,2759,2762,2765],{"className":2752},[638],[583,2754],{"className":2755,"style":990},[642],[583,2757,609],{"className":2758},[651,652],[583,2760],{"className":2761,"style":773},[656],[583,2763,971],{"className":2764},[777],[583,2766],{"className":2767,"style":773},[656],[583,2769,2771,2774],{"className":2770},[638],[583,2772],{"className":2773,"style":1925},[642],[583,2775,1225],{"className":2776},[651]," nicht definiert, die gekürzte Form gilt nur für ",[583,2779,2781,2800],{"className":2780},[586],[583,2782,2784],{"className":2783},[590],[592,2785,2786],{"xmlns":594},[596,2787,2788,2797],{},[599,2789,2790,2792,2795],{},[607,2791,609],{},[602,2793,2794],{"mathvariant":2668},"≠",[619,2796,1225],{},[626,2798,2799],{"encoding":628},"x \\neq 1",[583,2801,2803,2861],{"className":2802,"ariaHidden":634},[633],[583,2804,2806,2809,2812,2815,2858],{"className":2805},[638],[583,2807],{"className":2808,"style":1141},[642],[583,2810,609],{"className":2811},[651,652],[583,2813],{"className":2814,"style":773},[656],[583,2816,2818,2851,2855],{"className":2817},[777],[583,2819,2821],{"className":2820},[777],[583,2822,2825],{"className":2823},[651,2824],"vbox",[583,2826,2829],{"className":2827},[2828],"thinbox",[583,2830,2833,2836,2847],{"className":2831},[2832],"rlap",[583,2834],{"className":2835,"style":1141},[642],[583,2837,2840],{"className":2838},[2839],"inner",[583,2841,2843],{"className":2842},[651],[583,2844,2846],{"className":2845},[777],"",[583,2848],{"className":2849},[2850],"fix",[583,2852],{"className":2853},[656,2854],"nobreak",[583,2856,971],{"className":2857},[777],[583,2859],{"className":2860,"style":773},[656],[583,2862,2864,2867],{"className":2863},[638],[583,2865],{"className":2866,"style":1925},[642],[583,2868,1225],{"className":2869},[651],[576,2871,2872],{},"Jede Nennernullstelle als Polstelle bezeichnen, ohne zu prüfen, ob sie sich kürzen lässt.",[576,2874,2875,2876,2926],{},"Den Vorzeichenwechsel an der Vielfachheit im ursprünglichen Nenner ablesen statt an der Ordnung ",[583,2877,2879,2896],{"className":2878},[586],[583,2880,2882],{"className":2881},[590],[592,2883,2884],{"xmlns":594},[596,2885,2886,2894],{},[599,2887,2888,2890,2892],{},[607,2889,752],{},[602,2891,612],{},[607,2893,746],{},[626,2895,1082],{"encoding":628},[583,2897,2899,2917],{"className":2898,"ariaHidden":634},[633],[583,2900,2902,2905,2908,2911,2914],{"className":2901},[638],[583,2903],{"className":2904,"style":1092},[642],[583,2906,752],{"className":2907,"style":791},[651,652],[583,2909],{"className":2910,"style":657},[656],[583,2912,612],{"className":2913},[661],[583,2915],{"className":2916,"style":657},[656],[583,2918,2920,2923],{"className":2919},[638],[583,2921],{"className":2922,"style":787},[642],[583,2924,746],{"className":2925,"style":769},[651,652]," nach dem Kürzen.",{"title":2928,"searchDepth":2929,"depth":2929,"links":2930},"",2,[2931,2932,2933],{"id":561,"depth":2929,"text":562},{"id":1156,"depth":2929,"text":1157},{"id":2691,"depth":2929,"text":2692},[2935,2938,2941,2944,2946,2949,2951,2953],{"lhs":2936,"rhs":2937},"(x^2 - 1)\u002F(x^2 - 3*x + 2)","(x + 1)\u002F(x - 2)",{"lhs":2939,"rhs":2940},"(x - 1)*(x - 2)","x^2 - 3*x + 2",{"lhs":2942,"rhs":2943},"(1 + 1)\u002F(1 - 2)","-2",{"lhs":2945,"rhs":2943},"round((1.000001^2 - 1)\u002F(1.000001^2 - 3*1.000001 + 2), 4)",{"lhs":2947,"rhs":2948},"sign((1.99 + 1)\u002F(1.99 - 2))","-1",{"lhs":2950,"rhs":1225},"sign((2.01 + 1)\u002F(2.01 - 2))",{"lhs":2952,"rhs":1225},"sign(1\u002F(2.99 - 3)^2)",{"lhs":2954,"rhs":1225},"sign(1\u002F(3.01 - 3)^2)","u(x_0) \\neq 0,\\ v(x_0) \\neq 0,\\ l \\ge 1","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>u\u003C\u002Fmi>\u003Cmo 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\\\\ k \u003C l \\Rightarrow \\text{Polstelle} \\end{gathered}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmtable rowspacing=\"0.25em\" columnalign=\"center\" columnspacing=\"0em\">\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>f\u003C\u002Fmi>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmo stretchy=\"false\">(\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>−\u003C\u002Fmo>\u003Cmsub>\u003Cmi>x\u003C\u002Fmi>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsup>\u003Cmo stretchy=\"false\">)\u003C\u002Fmo>\u003Cmi>k\u003C\u002Fmi>\u003C\u002Fmsup>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmi>u\u003C\u002Fmi>\u003Cmo 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accent=\"true\">\u003Cmtext>u\u003C\u002Fmtext>\u003Cmo>¨\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmtext>cke\u003C\u002Fmtext>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003Cmtr>\u003Cmtd>\u003Cmstyle scriptlevel=\"0\" displaystyle=\"true\">\u003Cmrow>\u003Cmi>k\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmi>l\u003C\u002Fmi>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>Polstelle\u003C\u002Fmtext>\u003C\u002Fmrow>\u003C\u002Fmstyle>\u003C\u002Fmtd>\u003C\u002Fmtr>\u003C\u002Fmtable>\u003Cannotation encoding=\"application\u002Fx-tex\">\\begin{gathered} f(x) = \\frac{(x - x_0)^k \\cdot u(x)}{(x - x_0)^l \\cdot v(x)} \\\\ k \\ge l \\Rightarrow \\text{hebbare Lücke} \\\\ k < l \\Rightarrow \\text{Polstelle} \\end{gathered}\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:5.4621em;vertical-align:-2.4811em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mtable\">\u003Cspan class=\"col-align-c\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:2.9811em;\">\u003Cspan style=\"top:-4.9811em;\">\u003Cspan class=\"pstrut\" style=\"height:3.5261em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1076em;\">f\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t 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mtight\">0\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=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7751em;\">\u003Cspan style=\"top:-2.989em;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\" style=\"margin-right:0.0197em;\">l\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" 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class=\"mbin\">−\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\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 mtight\">0\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=\"mclose\">\u003Cspan class=\"mclose\">)\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.8491em;\">\u003Cspan style=\"top:-3.063em;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\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"mopen\">(\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mclose\">)\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:0.936em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-2.9051em;\">\u003Cspan class=\"pstrut\" style=\"height:3.5261em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">≥\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">hebbare L\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6679em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.25em;\">\u003Cspan class=\"mord\">¨\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mord\">cke\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-1.4051em;\">\u003Cspan class=\"pstrut\" style=\"height:3.5261em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\"><\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0197em;\">l\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">⇒\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mord text\">\u003Cspan class=\"mord\">Polstelle\u003C\u002Fspan>\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:2.4811em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},"\u002Fde\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpolstellen-und-hebbare-luecken",[],[3015,3016,3017,3018],"rational-function-asymptotes","polynomial-division","zero-product","quadratic-factored-form",{"title":548,"description":2928},"de\u002Fformulas\u002Fmath\u002Ffunctions\u002Fpolstellen-und-hebbare-luecken","Eine Nennernullstelle ist eine hebbare Lücke, wenn sie sich vollständig wegkürzen lässt, sonst eine Polstelle.",[3023,3024,3025,3026,3027],"polstelle","definitionslücke","gebrochenrationale funktion","asymptote","kürzen",[3029,3033,3036,3039],{"symbol":3030,"meaning":3031,"symbolHtml":3032},"x_0","Nullstelle des Nenners, also eine Definitionslücke","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath 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