簡約 (\frac{16)/(x-2)}{4/(x+1)+6/x}

解

簡約

\frac{\frac{16}{x - 2}}{\frac{4}{x + 1} + \frac{6}{x}}

\frac{8 x ( x + 1 )}{( x - 2 ) ( 5 x + 3 )}

解答ステップ

\frac{\frac{16}{x - 2}}{\frac{4}{x + 1} + \frac{6}{x}}

分数の規則を適用する:

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

= \frac{16}{( x - 2 ) ( \frac{4}{x + 1} + \frac{6}{x} )}

簡素化

(x - 2) (\frac{4}{x + 1} + \frac{6}{x}) : \frac{( x - 2 ) ( 10 x + 6 )}{x ( x + 1 )}

= \frac{16}{\frac{( x - 2 ) ( 10 x + 6 )}{x ( x + 1 )}}

分数の規則を適用する:

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

= \frac{16 x ( x + 1 )}{( x - 2 ) ( 10 x + 6 )}

キャンセル

\frac{16 x ( x + 1 )}{( x - 2 ) ( 10 x + 6 )} : \frac{8 x ( x + 1 )}{( x - 2 ) ( 5 x + 3 )}

= \frac{8 x ( x + 1 )}{( x - 2 ) ( 5 x + 3 )}