miniaufgabe.js
==== 2. April 2018 bis 6. April 2018 ====
=== Dienstag 3. April 2018 ===
Prüfung, keine Miniaufgabe.
=== Freitag 6. April 2018 ===
Zusammenfassen, ausklammern, kürzen, Resultat als Vielfaches einer Potenz von $x$:
miniAufgabe("#exovereinfachenAusklammern","#solvereinfachenAusklammern",
[["$\\displaystyle \\frac{\\frac{5}{9} \\cdot x^{-5} \\cdot \\frac{1}{x^{-9}} +\\frac{1}{3} \\cdot x^{5} \\cdot \\frac{1}{x^{-4}}}{\\frac{4}{5} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}} +\\frac{12}{25} \\cdot x^{3} \\cdot \\frac{1}{x^{-18}}}$", "$\\displaystyle \\frac{\\frac{5}{9}\\cdot x^{4} +\\frac{1}{3}\\cdot x^{9}}{\\frac{4}{5}\\cdot x^{16} +\\frac{12}{25}\\cdot x^{21}} = \\frac{\\frac{1}{9}\\cdot x^{4} \\cdot \\left(5 +3\\cdot x^{5}\\right)}{\\frac{4}{25}\\cdot x^{16} \\cdot \\left(5 +3\\cdot x^{5}\\right)} = \\frac{1}{9} \\cdot \\frac{25}{4} \\cdot x^{-12} = \\frac{25}{36}\\cdot x^{-12}$"], ["$\\displaystyle \\frac{\\frac{4}{9} \\cdot x^{6} \\cdot \\frac{1}{x^{-9}} +\\frac{2}{9} \\cdot x^{3} \\cdot \\frac{1}{x^{-4}}}{\\frac{1}{7} \\cdot x^{7} \\cdot \\frac{1}{x^{2}} +\\frac{1}{14} \\cdot x^{6} \\cdot \\frac{1}{x^{9}}}$", "$\\displaystyle \\frac{\\frac{4}{9}\\cdot x^{15} +\\frac{2}{9}\\cdot x^{7}}{\\frac{1}{7}\\cdot x^{5} +\\frac{1}{14}\\cdot x^{-3}} = \\frac{\\frac{2}{9}\\cdot x^{7} \\cdot \\left(2\\cdot x^{8} +1\\right)}{\\frac{1}{14}\\cdot x^{-3} \\cdot \\left(2\\cdot x^{8} +1\\right)} = \\frac{2}{9} \\cdot 14 \\cdot x^{10} = \\frac{28}{9}\\cdot x^{10}$"], ["$\\displaystyle \\frac{\\frac{7}{5} \\cdot x^{6} \\cdot \\frac{1}{x^{-4}} +\\frac{5}{3} \\cdot x^{5} \\cdot \\frac{1}{x^{-8}}}{\\frac{3}{4} \\cdot x^{2} \\cdot \\frac{1}{x^{-6}} +\\frac{25}{28} \\cdot x^{6} \\cdot \\frac{1}{x^{-5}}}$", "$\\displaystyle \\frac{\\frac{7}{5}\\cdot x^{10} +\\frac{5}{3}\\cdot x^{13}}{\\frac{3}{4}\\cdot x^{8} +\\frac{25}{28}\\cdot x^{11}} = \\frac{\\frac{1}{15}\\cdot x^{10} \\cdot \\left(21 +25\\cdot x^{3}\\right)}{\\frac{1}{28}\\cdot x^{8} \\cdot \\left(21 +25\\cdot x^{3}\\right)} = \\frac{1}{15} \\cdot 28 \\cdot x^{2} = \\frac{28}{15}\\cdot x^{2}$"], ["$\\displaystyle \\frac{\\frac{2}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}} +\\frac{1}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{2}}}{\\frac{3}{5} \\cdot x^{3} \\cdot \\frac{1}{x^{-6}} +\\frac{3}{10} \\cdot x^{-3} \\cdot \\frac{1}{x^{-2}}}$", "$\\displaystyle \\frac{\\frac{2}{3}\\cdot x^{16} +\\frac{1}{3}\\cdot x^{6}}{\\frac{3}{5}\\cdot x^{9} +\\frac{3}{10}\\cdot x^{-1}} = \\frac{\\frac{1}{3}\\cdot x^{6} \\cdot \\left(2\\cdot x^{10} +1\\right)}{\\frac{3}{10}\\cdot x^{-1} \\cdot \\left(2\\cdot x^{10} +1\\right)} = \\frac{1}{3} \\cdot \\frac{10}{3} \\cdot x^{7} = \\frac{10}{9}\\cdot x^{7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{2} \\cdot \\frac{1}{x^{-3}} +\\frac{3}{8} \\cdot x^{9} \\cdot \\frac{1}{x^{-8}}}{\\frac{1}{2} \\cdot x^{4} \\cdot \\frac{1}{x^{-5}} +\\frac{1}{8} \\cdot x^{5} \\cdot \\frac{1}{x^{-16}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{5} +\\frac{3}{8}\\cdot x^{17}}{\\frac{1}{2}\\cdot x^{9} +\\frac{1}{8}\\cdot x^{21}} = \\frac{\\frac{3}{8}\\cdot x^{5} \\cdot \\left(4 +1\\cdot x^{12}\\right)}{\\frac{1}{8}\\cdot x^{9} \\cdot \\left(4 +1\\cdot x^{12}\\right)} = \\frac{3}{8} \\cdot 8 \\cdot x^{-4} = 3\\cdot x^{-4}$"], ["$\\displaystyle \\frac{\\frac{1}{4} \\cdot x^{6} \\cdot \\frac{1}{x^{-4}} +\\frac{9}{5} \\cdot x^{6} \\cdot \\frac{1}{x^{-9}}}{\\frac{7}{2} \\cdot x^{9} \\cdot \\frac{1}{x^{5}} +\\frac{126}{5} \\cdot x^{-4} \\cdot \\frac{1}{x^{-13}}}$", "$\\displaystyle \\frac{\\frac{1}{4}\\cdot x^{10} +\\frac{9}{5}\\cdot x^{15}}{\\frac{7}{2}\\cdot x^{4} +\\frac{126}{5}\\cdot x^{9}} = \\frac{\\frac{1}{20}\\cdot x^{10} \\cdot \\left(5 +36\\cdot x^{5}\\right)}{\\frac{7}{10}\\cdot x^{4} \\cdot \\left(5 +36\\cdot x^{5}\\right)} = \\frac{1}{20} \\cdot \\frac{10}{7} \\cdot x^{6} = \\frac{1}{14}\\cdot x^{6}$"], ["$\\displaystyle \\frac{\\frac{9}{7} \\cdot x^{3} \\cdot \\frac{1}{x^{-2}} +\\frac{9}{4} \\cdot x^{5} \\cdot \\frac{1}{x^{-6}}}{\\frac{4}{5} \\cdot x^{7} \\cdot \\frac{1}{x^{-5}} +\\frac{7}{5} \\cdot x^{8} \\cdot \\frac{1}{x^{-10}}}$", "$\\displaystyle \\frac{\\frac{9}{7}\\cdot x^{5} +\\frac{9}{4}\\cdot x^{11}}{\\frac{4}{5}\\cdot x^{12} +\\frac{7}{5}\\cdot x^{18}} = \\frac{\\frac{9}{28}\\cdot x^{5} \\cdot \\left(4 +7\\cdot x^{6}\\right)}{\\frac{1}{5}\\cdot x^{12} \\cdot \\left(4 +7\\cdot x^{6}\\right)} = \\frac{9}{28} \\cdot 5 \\cdot x^{-7} = \\frac{45}{28}\\cdot x^{-7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{9} \\cdot \\frac{1}{x^{4}} +\\frac{1}{3} \\cdot x^{8} \\cdot \\frac{1}{x^{-8}}}{\\frac{5}{2} \\cdot x^{3} \\cdot \\frac{1}{x^{-9}} +\\frac{5}{9} \\cdot x^{8} \\cdot \\frac{1}{x^{-15}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{5} +\\frac{1}{3}\\cdot x^{16}}{\\frac{5}{2}\\cdot x^{12} +\\frac{5}{9}\\cdot x^{23}} = \\frac{\\frac{1}{6}\\cdot x^{5} \\cdot \\left(9 +2\\cdot x^{11}\\right)}{\\frac{5}{18}\\cdot x^{12} \\cdot \\left(9 +2\\cdot x^{11}\\right)} = \\frac{1}{6} \\cdot \\frac{18}{5} \\cdot x^{-7} = \\frac{3}{5}\\cdot x^{-7}$"], ["$\\displaystyle \\frac{\\frac{3}{2} \\cdot x^{2} \\cdot \\frac{1}{x^{-6}} +\\frac{1}{8} \\cdot x^{5} \\cdot \\frac{1}{x^{-6}}}{\\frac{8}{7} \\cdot x^{7} \\cdot \\frac{1}{x^{3}} +\\frac{2}{21} \\cdot x^{-3} \\cdot \\frac{1}{x^{-10}}}$", "$\\displaystyle \\frac{\\frac{3}{2}\\cdot x^{8} +\\frac{1}{8}\\cdot x^{11}}{\\frac{8}{7}\\cdot x^{4} +\\frac{2}{21}\\cdot x^{7}} = \\frac{\\frac{1}{8}\\cdot x^{8} \\cdot \\left(12 +1\\cdot x^{3}\\right)}{\\frac{2}{21}\\cdot x^{4} \\cdot \\left(12 +1\\cdot x^{3}\\right)} = \\frac{1}{8} \\cdot \\frac{21}{2} \\cdot x^{4} = \\frac{21}{16}\\cdot x^{4}$"], ["$\\displaystyle \\frac{\\frac{1}{2} \\cdot x^{6} \\cdot \\frac{1}{x^{-5}} +\\frac{5}{7} \\cdot x^{8} \\cdot \\frac{1}{x^{3}}}{\\frac{1}{7} \\cdot x^{-3} \\cdot \\frac{1}{x^{-7}} +\\frac{10}{49} \\cdot x^{2} \\cdot \\frac{1}{x^{4}}}$", "$\\displaystyle \\frac{\\frac{1}{2}\\cdot x^{11} +\\frac{5}{7}\\cdot x^{5}}{\\frac{1}{7}\\cdot x^{4} +\\frac{10}{49}\\cdot x^{-2}} = \\frac{\\frac{1}{14}\\cdot x^{5} \\cdot \\left(7\\cdot x^{6} +10\\right)}{\\frac{1}{49}\\cdot x^{-2} \\cdot \\left(7\\cdot x^{6} +10\\right)} = \\frac{1}{14} \\cdot 49 \\cdot x^{7} = \\frac{7}{2}\\cdot x^{7}$"]],
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