簡約 (2/b-5/(b+3))/(3/b+3/(b+3))

解

簡約

\frac{\frac{2}{b} - \frac{5}{b + 3}}{\frac{3}{b} + \frac{3}{b + 3}}

\frac{- b + 2}{2 b + 3}

解答ステップ

\frac{\frac{2}{b} - \frac{5}{b + 3}}{\frac{3}{b} + \frac{3}{b + 3}}

結合

\frac{2}{b} - \frac{5}{b + 3} : \frac{- 3 b + 6}{b ( b + 3 )}

= \frac{\frac{- 3 b + 6}{b ( b + 3 )}}{\frac{3}{b} + \frac{3}{b + 3}}

結合

\frac{3}{b} + \frac{3}{b + 3} : \frac{6 b + 9}{b ( b + 3 )}

= \frac{\frac{- 3 b + 6}{b ( b + 3 )}}{\frac{6 b + 9}{b ( b + 3 )}}

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{( - 3 b + 6 ) b ( b + 3 )}{b ( b + 3 ) ( 6 b + 9 )}

キャンセル

\frac{( - 3 b + 6 ) b ( b + 3 )}{b ( b + 3 ) ( 6 b + 9 )} : \frac{- b + 2}{2 b + 3}

= \frac{- b + 2}{2 b + 3}