簡約 (2/(1-a)+2/(1+a))/(2/(1+a)-2/(1-a))

解

簡約

\frac{\frac{2}{1 - a} + \frac{2}{1 + a}}{\frac{2}{1 + a} - \frac{2}{1 - a}}

- \frac{1}{a}

解答ステップ

\frac{\frac{2}{1 - a} + \frac{2}{1 + a}}{\frac{2}{1 + a} - \frac{2}{1 - a}}

結合

\frac{2}{1 - a} + \frac{2}{1 + a} : \frac{4}{( - a + 1 ) ( a + 1 )}

= \frac{\frac{4}{( - a + 1 ) ( a + 1 )}}{\frac{2}{1 + a} - \frac{2}{1 - a}}

結合

\frac{2}{1 + a} - \frac{2}{1 - a} : - \frac{4 a}{( a + 1 ) ( - a + 1 )}

= \frac{\frac{4}{( - a + 1 ) ( a + 1 )}}{- \frac{4 a}{( a + 1 ) ( - a + 1 )}}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{4}{( - a + 1 ) ( a + 1 )}}{\frac{4 a}{( a + 1 ) ( - a + 1 )}}

分数の規則を適用する:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

\frac{\frac{4}{( - a + 1 ) ( a + 1 )}}{\frac{4 a}{( a + 1 ) ( - a + 1 )}} = \frac{4 ( a + 1 ) ( - a + 1 )}{( - a + 1 ) ( a + 1 ) \cdot 4 a}

= - \frac{4 ( a + 1 ) ( - a + 1 )}{( - a + 1 ) ( a + 1 ) \cdot 4 a}

キャンセル

- \frac{4 ( a + 1 ) ( - a + 1 )}{( - a + 1 ) ( a + 1 ) \cdot 4 a} : - \frac{1}{a}

= - \frac{1}{a}