展開する (2(-x^2-3))/(9(x^2-1)^{5/3)}

解

展開する

\frac{2 ( - x ^{2} - 3 )}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

- \frac{2 x ^{2}}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}} - \frac{2}{3 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

解答ステップ

\frac{2 ( - x ^{2} - 3 )}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

拡張

2 (- x^{2} - 3) : - 2 x^{2} - 6

= \frac{- 2 x ^{2} - 6}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 2 x ^{2} - 6}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}} = - \frac{2 x ^{2}}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}} - \frac{6}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

= - \frac{2 x ^{2}}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}} - \frac{6}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

キャンセル

\frac{6}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}} : \frac{2}{3 ( x ^{2} - 1 ) ^{\frac{5}{3}}}

= - \frac{2 x ^{2}}{9 ( x ^{2} - 1 ) ^{\frac{5}{3}}} - \frac{2}{3 ( x ^{2} - 1 ) ^{\frac{5}{3}}}