簡約 1/(x-3)+1/(x+3)-2/x

解

簡約

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

\frac{18}{x ( x - 3 ) ( x + 3 )}

解答ステップ

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

以下の最小公倍数:

x - 3, x + 3, x : x (x - 3) (x + 3)

LCMに基づいて分数を調整する

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

分数の規則を適用する:

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

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

簡素化

x (x + 3) + x (x - 3) - 2 (x - 3) (x + 3) : 18

= \frac{18}{x ( x - 3 ) ( x + 3 )}