簡約 1/x-2/(x^2+x)-3/(x+3)

解

簡約

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

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

解答ステップ

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

以下の最小公倍数:

x, x^{2} + x, x + 3 : x (x + 1) (x + 3)

LCMに基づいて分数を調整する

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

分数の規則を適用する:

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

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

簡素化

(x + 1) (x + 3) - 2 (x + 3) - 3 x (x + 1) : - 2 x^{2} - x - 3

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