簡約 (2ab)/(a^2-b^2)-b/(a-b)+4/2

解

簡約

\frac{2 ab}{a ^{2} - b ^{2}} - \frac{b}{a - b} + \frac{4}{2}

\frac{- a ^{2} b - 4 a b ^{2} + 3 b ^{3} + 2 a ^{3}}{( a - b ) ( a ^{2} - b ^{2} )}

解答ステップ

\frac{2 ab}{a ^{2} - b ^{2}} - \frac{b}{a - b} + \frac{4}{2}

以下の最小公倍数:

a^{2} - b^{2}, a - b, 2 : 2 (a - b) (a^{2} - b^{2})

LCMに基づいて分数を調整する

= \frac{4 ab ( a - b )}{2 ( a - b ) ( a ^{2} - b ^{2} )} - \frac{b \cdot 2 ( a ^{2} - b ^{2} )}{2 ( a - b ) ( a ^{2} - b ^{2} )} + \frac{4 ( a - b ) ( a ^{2} - b ^{2} )}{2 ( a - b ) ( a ^{2} - b ^{2} )}

分数の規則を適用する:

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

= \frac{4 ab ( a - b ) - b \cdot 2 ( a ^{2} - b ^{2} ) + 4 ( a - b ) ( a ^{2} - b ^{2} )}{2 ( a - b ) ( a ^{2} - b ^{2} )}

簡素化

4 ab (a - b) - b \cdot 2 (a^{2} - b^{2}) + 4 (a - b) (a^{2} - b^{2}) : - 2 a^{2} b - 8 a b^{2} + 6 b^{3} + 4 a^{3}

= \frac{- 2 a ^{2} b - 8 a b ^{2} + 6 b ^{3} + 4 a ^{3}}{2 ( a - b ) ( a ^{2} - b ^{2} )}

キャンセル

\frac{- 2 a ^{2} b - 8 a b ^{2} + 6 b ^{3} + 4 a ^{3}}{2 ( a - b ) ( a ^{2} - b ^{2} )} : \frac{- a ^{2} b - 4 a b ^{2} + 3 b ^{3} + 2 a ^{3}}{( a - b ) ( a ^{2} - b ^{2} )}

= \frac{- a ^{2} b - 4 a b ^{2} + 3 b ^{3} + 2 a ^{3}}{( a - b ) ( a ^{2} - b ^{2} )}