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受欢迎的代数 >

化简 (x^5-5x^3+4x)/(x+2)

解答

化简

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

解答

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

求解步骤

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

因式分解

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

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

令

u = x^{2}

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

因式分解

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

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

u = x^{2}

代回

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

因式分解

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

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

因式分解

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

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

约分:

x + 2

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

流行的例子

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s im pl i f y tan (x) (1 + cos (x)) - sin^{2} (x) csc (x)

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s im pl i f y cot (x) - \frac{csc ^{2} ( x )}{cot ( x )}

因式分解-2x+10

f a c t or - 2 x + 10

化简 ln(1/(e^{10)})

s im pl i f y ln (\frac{1}{e ^{10}})

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s im pl i f y lo g_{6} (6^{2})