展開する (2(-x+8))/(5e^{x/(10))x^{1/5}}

解

展開する

\frac{2 ( - x + 8 )}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

- \frac{2 x ^{\frac{4}{5}}}{5 e ^{\frac{x}{10}}} + \frac{16}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

解答ステップ

\frac{2 ( - x + 8 )}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

拡張

2 (- x + 8) : - 2 x + 16

= \frac{- 2 x + 16}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

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 + 16}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}} = - \frac{2 x}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}} + \frac{16}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

= - \frac{2 x}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}} + \frac{16}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}

キャンセル

\frac{2 x}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}} : \frac{2 x ^{\frac{4}{5}}}{5 e ^{\frac{x}{10}}}

= - \frac{2 x ^{\frac{4}{5}}}{5 e ^{\frac{x}{10}}} + \frac{16}{5 e ^{\frac{x}{10}} x ^{\frac{1}{5}}}