What is (x^5-5x^3+4x)/(x+2) ?

The solution to (x^5-5x^3+4x)/(x+2) is x(x+1)(x-1)(x-2)

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simplify (x^5-5x^3+4x)/(x+2)

simplify

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

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

Solution steps

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

Factor

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

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

Let

u = x^{2}

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

Factor

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

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

Substitute back

u = x^{2}

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

Factor

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

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

Factor

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

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

Cancel the common factor:

x + 2

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

tan (x) (1 + cos (x)) - sin^{2} (x) csc (x)

(x + y)^{8}

cot (x) - \frac{csc ^{2} ( x )}{cot ( x )}

0. 5^{8}

- 2 x + 10

What is (x^5-5x^3+4x)/(x+2) ?
The solution to (x^5-5x^3+4x)/(x+2) is x(x+1)(x-1)(x-2)