簡約 (x+2)/(x-4)+2/x+(5x)/(3x-1)

解

簡約

\frac{x + 2}{x - 4} + \frac{2}{x} + \frac{5 x}{3 x - 1}

\frac{8 x ^{3} - 9 x ^{2} - 28 x + 8}{x ( x - 4 ) ( 3 x - 1 )}

解答ステップ

\frac{x + 2}{x - 4} + \frac{2}{x} + \frac{5 x}{3 x - 1}

以下の最小公倍数:

x - 4, x, 3 x - 1 : x (x - 4) (3 x - 1)

LCMに基づいて分数を調整する

= \frac{( x + 2 ) x ( 3 x - 1 )}{x ( x - 4 ) ( 3 x - 1 )} + \frac{2 ( x - 4 ) ( 3 x - 1 )}{x ( x - 4 ) ( 3 x - 1 )} + \frac{5 x ^{2} ( x - 4 )}{x ( x - 4 ) ( 3 x - 1 )}

分数の規則を適用する:

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

= \frac{( x + 2 ) x ( 3 x - 1 ) + 2 ( x - 4 ) ( 3 x - 1 ) + 5 x ^{2} ( x - 4 )}{x ( x - 4 ) ( 3 x - 1 )}

簡素化

(x + 2) x (3 x - 1) + 2 (x - 4) (3 x - 1) + 5 x^{2} (x - 4) : 8 x^{3} - 9 x^{2} - 28 x + 8

= \frac{8 x ^{3} - 9 x ^{2} - 28 x + 8}{x ( x - 4 ) ( 3 x - 1 )}