miniaufgabe.js ==== 4. April 2022 bis 8. April 2022 ==== === Donnerstag 7. April 2022 === Fassen Sie auf einen Bruchstrich zusammen und kürzen Sie soweit als möglich.miniAufgabe("#exobruchtermvereinfachen","#solbruchtermvereinfachen", [["$\\displaystyle \\frac{4k}{5f-k}+\\frac{-45fk-9k^{2}}{25f^{2}-k^{2}}$", "$\\begin{multline*}\\frac{4k}{5f-k}+\\frac{-45fk-9k^{2}}{25f^{2}-k^{2}} = \\frac{4k}{5f-k}+\\frac{-45fk-9k^{2}}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{\\left(5f+k\\right) \\cdot 4k}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)}+\\frac{-45fk-9k^{2}}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\\\ \\frac{20fk-45fk+4k^{2}-9k^{2}}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{-25fk-5k^{2}}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{-5k \\cdot \\left(5f+k\\right)}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{-5k}{5f-k}\\end{multline*}$"], ["$\\displaystyle \\frac{4p}{3d+p}+\\frac{-27dp+9p^{2}}{9d^{2}-p^{2}}$", "$\\begin{multline*}\\frac{4p}{3d+p}+\\frac{-27dp+9p^{2}}{9d^{2}-p^{2}} = \\frac{4p}{3d+p}+\\frac{-27dp+9p^{2}}{\\left(3d+p\\right) \\cdot \\left(3d-p\\right)} = \\frac{\\left(3d-p\\right) \\cdot 4p}{\\left(3d+p\\right) \\cdot \\left(3d-p\\right)}+\\frac{-27dp+9p^{2}}{\\left(3d+p\\right) \\cdot \\left(3d-p\\right)} = \\\\ \\frac{12dp-27dp+9p^{2}-4p^{2}}{\\left(3d+p\\right) \\cdot \\left(3d-p\\right)} = \\frac{-15dp+5p^{2}}{\\left(3d+p\\right) \\cdot \\left(3d-p\\right)} = \\frac{-5p \\cdot \\left(3d-p\\right)}{\\left(3d+p\\right) \\cdot \\left(3d-p\\right)} = \\frac{-5p}{3d+p}\\end{multline*}$"], ["$\\displaystyle \\frac{-4e}{5b+e}+\\frac{-10be+2e^{2}}{25b^{2}-e^{2}}$", "$\\begin{multline*}\\frac{-4e}{5b+e}+\\frac{-10be+2e^{2}}{25b^{2}-e^{2}} = \\frac{-4e}{5b+e}+\\frac{-10be+2e^{2}}{\\left(5b+e\\right) \\cdot \\left(5b-e\\right)} = \\frac{\\left(5b-e\\right) \\cdot -4e}{\\left(5b+e\\right) \\cdot \\left(5b-e\\right)}+\\frac{-10be+2e^{2}}{\\left(5b+e\\right) \\cdot \\left(5b-e\\right)} = \\\\ \\frac{-10be-20be+4e^{2}+2e^{2}}{\\left(5b+e\\right) \\cdot \\left(5b-e\\right)} = \\frac{-30be+6e^{2}}{\\left(5b+e\\right) \\cdot \\left(5b-e\\right)} = \\frac{-6e \\cdot \\left(5b-e\\right)}{\\left(5b+e\\right) \\cdot \\left(5b-e\\right)} = \\frac{-6e}{5b+e}\\end{multline*}$"], ["$\\displaystyle \\frac{3n}{2k-n}+\\frac{6kn+3n^{2}}{4k^{2}-n^{2}}$", "$\\begin{multline*}\\frac{3n}{2k-n}+\\frac{6kn+3n^{2}}{4k^{2}-n^{2}} = \\frac{3n}{2k-n}+\\frac{6kn+3n^{2}}{\\left(2k-n\\right) \\cdot \\left(2k+n\\right)} = \\frac{\\left(2k+n\\right) \\cdot 3n}{\\left(2k-n\\right) \\cdot \\left(2k+n\\right)}+\\frac{6kn+3n^{2}}{\\left(2k-n\\right) \\cdot \\left(2k+n\\right)} = \\\\ \\frac{6kn+6kn+3n^{2}+3n^{2}}{\\left(2k-n\\right) \\cdot \\left(2k+n\\right)} = \\frac{12kn+6n^{2}}{\\left(2k-n\\right) \\cdot \\left(2k+n\\right)} = \\frac{6n \\cdot \\left(2k+n\\right)}{\\left(2k-n\\right) \\cdot \\left(2k+n\\right)} = \\frac{6n}{2k-n}\\end{multline*}$"], ["$\\displaystyle \\frac{6c}{2b-c}+\\frac{-2bc-c^{2}}{4b^{2}-c^{2}}$", "$\\begin{multline*}\\frac{6c}{2b-c}+\\frac{-2bc-c^{2}}{4b^{2}-c^{2}} = \\frac{6c}{2b-c}+\\frac{-2bc-c^{2}}{\\left(2b-c\\right) \\cdot \\left(2b+c\\right)} = \\frac{\\left(2b+c\\right) \\cdot 6c}{\\left(2b-c\\right) \\cdot \\left(2b+c\\right)}+\\frac{-2bc-c^{2}}{\\left(2b-c\\right) \\cdot \\left(2b+c\\right)} = \\\\ \\frac{12bc-2bc+6c^{2}-c^{2}}{\\left(2b-c\\right) \\cdot \\left(2b+c\\right)} = \\frac{10bc+5c^{2}}{\\left(2b-c\\right) \\cdot \\left(2b+c\\right)} = \\frac{5c \\cdot \\left(2b+c\\right)}{\\left(2b-c\\right) \\cdot \\left(2b+c\\right)} = \\frac{5c}{2b-c}\\end{multline*}$"], ["$\\displaystyle \\frac{4h}{3a+h}+\\frac{-3ah+h^{2}}{9a^{2}-h^{2}}$", "$\\begin{multline*}\\frac{4h}{3a+h}+\\frac{-3ah+h^{2}}{9a^{2}-h^{2}} = \\frac{4h}{3a+h}+\\frac{-3ah+h^{2}}{\\left(3a+h\\right) \\cdot \\left(3a-h\\right)} = \\frac{\\left(3a-h\\right) \\cdot 4h}{\\left(3a+h\\right) \\cdot \\left(3a-h\\right)}+\\frac{-3ah+h^{2}}{\\left(3a+h\\right) \\cdot \\left(3a-h\\right)} = \\\\ \\frac{12ah-3ah+h^{2}-4h^{2}}{\\left(3a+h\\right) \\cdot \\left(3a-h\\right)} = \\frac{9ah-3h^{2}}{\\left(3a+h\\right) \\cdot \\left(3a-h\\right)} = \\frac{3h \\cdot \\left(3a-h\\right)}{\\left(3a+h\\right) \\cdot \\left(3a-h\\right)} = \\frac{3h}{3a+h}\\end{multline*}$"], ["$\\displaystyle \\frac{-6k}{5f-k}+\\frac{0}{25f^{2}-k^{2}}$", "$\\begin{multline*}\\frac{-6k}{5f-k}+\\frac{0}{25f^{2}-k^{2}} = \\frac{-6k}{5f-k}+\\frac{0}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{\\left(5f+k\\right) \\cdot -6k}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)}+\\frac{0}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\\\ \\frac{-30fk-6k^{2}}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{-30fk-6k^{2}}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{-6k \\cdot \\left(5f+k\\right)}{\\left(5f-k\\right) \\cdot \\left(5f+k\\right)} = \\frac{-6k}{5f-k}\\end{multline*}$"], ["$\\displaystyle \\frac{-6m}{2c-m}+\\frac{8cm+4m^{2}}{4c^{2}-m^{2}}$", "$\\begin{multline*}\\frac{-6m}{2c-m}+\\frac{8cm+4m^{2}}{4c^{2}-m^{2}} = \\frac{-6m}{2c-m}+\\frac{8cm+4m^{2}}{\\left(2c-m\\right) \\cdot \\left(2c+m\\right)} = \\frac{\\left(2c+m\\right) \\cdot -6m}{\\left(2c-m\\right) \\cdot \\left(2c+m\\right)}+\\frac{8cm+4m^{2}}{\\left(2c-m\\right) \\cdot \\left(2c+m\\right)} = \\\\ \\frac{8cm-12cm+4m^{2}-6m^{2}}{\\left(2c-m\\right) \\cdot \\left(2c+m\\right)} = \\frac{-4cm-2m^{2}}{\\left(2c-m\\right) \\cdot \\left(2c+m\\right)} = \\frac{-2m \\cdot \\left(2c+m\\right)}{\\left(2c-m\\right) \\cdot \\left(2c+m\\right)} = \\frac{-2m}{2c-m}\\end{multline*}$"], ["$\\displaystyle \\frac{-5w}{5c-w}+\\frac{-5cw-w^{2}}{25c^{2}-w^{2}}$", "$\\begin{multline*}\\frac{-5w}{5c-w}+\\frac{-5cw-w^{2}}{25c^{2}-w^{2}} = \\frac{-5w}{5c-w}+\\frac{-5cw-w^{2}}{\\left(5c-w\\right) \\cdot \\left(5c+w\\right)} = \\frac{\\left(5c+w\\right) \\cdot -5w}{\\left(5c-w\\right) \\cdot \\left(5c+w\\right)}+\\frac{-5cw-w^{2}}{\\left(5c-w\\right) \\cdot \\left(5c+w\\right)} = \\\\ \\frac{-5cw-25cw-w^{2}-5w^{2}}{\\left(5c-w\\right) \\cdot \\left(5c+w\\right)} = \\frac{-30cw-6w^{2}}{\\left(5c-w\\right) \\cdot \\left(5c+w\\right)} = \\frac{-6w \\cdot \\left(5c+w\\right)}{\\left(5c-w\\right) \\cdot \\left(5c+w\\right)} = \\frac{-6w}{5c-w}\\end{multline*}$"], ["$\\displaystyle \\frac{-5n}{4f-n}+\\frac{-4fn-n^{2}}{16f^{2}-n^{2}}$", "$\\begin{multline*}\\frac{-5n}{4f-n}+\\frac{-4fn-n^{2}}{16f^{2}-n^{2}} = \\frac{-5n}{4f-n}+\\frac{-4fn-n^{2}}{\\left(4f-n\\right) \\cdot \\left(4f+n\\right)} = \\frac{\\left(4f+n\\right) \\cdot -5n}{\\left(4f-n\\right) \\cdot \\left(4f+n\\right)}+\\frac{-4fn-n^{2}}{\\left(4f-n\\right) \\cdot \\left(4f+n\\right)} = \\\\ \\frac{-4fn-20fn-n^{2}-5n^{2}}{\\left(4f-n\\right) \\cdot \\left(4f+n\\right)} = \\frac{-24fn-6n^{2}}{\\left(4f-n\\right) \\cdot \\left(4f+n\\right)} = \\frac{-6n \\cdot \\left(4f+n\\right)}{\\left(4f-n\\right) \\cdot \\left(4f+n\\right)} = \\frac{-6n}{4f-n}\\end{multline*}$"]], "
", "
");
ruby bruchterme-vereinfachen.rb 1
 === Freitag 8. April 2022 === Prüfung. Keine Miniaufgabe