簡約 (x/2-1/(x+1))/(x/2+\frac{2x+3){x+1}}

解

簡約

\frac{\frac{x}{2} - \frac{1}{x + 1}}{\frac{x}{2} + \frac{2 x + 3}{x + 1}}

\frac{x - 1}{x + 3}

解答ステップ

\frac{\frac{x}{2} - \frac{1}{x + 1}}{\frac{x}{2} + \frac{2 x + 3}{x + 1}}

結合

\frac{x}{2} - \frac{1}{x + 1} : \frac{x ^{2} + x - 2}{2 ( x + 1 )}

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

結合

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

= \frac{\frac{x ^{2} + x - 2}{2 ( x + 1 )}}{\frac{x ^{2} + 5 x + 6}{2 ( x + 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{( x ^{2} + x - 2 ) \cdot 2 ( x + 1 )}{2 ( x + 1 ) ( x ^{2} + 5 x + 6 )}

キャンセル

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

= \frac{x - 1}{x + 3}