簡約 (x^5-5x^3+4x)/(x+2)

解

簡約

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

x (x + 1) (x - 1) (x - 2)

解答ステップ

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

因数

x^{5} - 5 x^{3} + 4 x : x (x^{4} - 5 x^{2} + 4)

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

u =

にする

x^{2}

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

因数

u^{2} - 5 u + 4 : (u - 1) (u - 4)

= \frac{x ( u - 1 ) ( u - 4 )}{x + 2}

代用を戻す

u = x^{2}

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

因数

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

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

因数

x^{2} - 4 : (x + 2) (x - 2)

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

共通因数を約分する:

x + 2

= x (x + 1) (x - 1) (x - 2)