What is expand 1/((x+1)^2(x-2)^3) ?

The solution to expand 1/((x+1)^2(x-2)^3) is 1/(x^5-4x^4+x^3+10x^2-4x-8)

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expand 1/((x+1)^2(x-2)^3)

expand

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

\frac{1}{x ^{5} - 4 x ^{4} + x ^{3} + 10 x ^{2} - 4 x - 8}

Solution steps

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

(x + 1)^{2} = x^{2} + 2 x + 1

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

(x - 2)^{3} = x^{3} - 6 x^{2} + 12 x - 8

= \frac{1}{( x ^{2} + 2 x + 1 ) ( x ^{3} - 6 x ^{2} + 12 x - 8 )}

Expand

(x^{2} + 2 x + 1) (x^{3} - 6 x^{2} + 12 x - 8) : x^{5} - 4 x^{4} + x^{3} + 10 x^{2} - 4 x - 8

= \frac{1}{x ^{5} - 4 x ^{4} + x ^{3} + 10 x ^{2} - 4 x - 8}

(x + y = 2,) (x^{(2)} + y^{(2)} = 4)

- e^{t} \cdot (2 e^{t} + 8 t e^{t})

x y d y (y + 1) (1 - x) d x

y (2 x^{2} - x y + y^{2}) d x

\frac{1}{2 ( 4 x - 10 ) ( 2 x + 3 )}

What is expand 1/((x+1)^2(x-2)^3) ?
The solution to expand 1/((x+1)^2(x-2)^3) is 1/(x^5-4x^4+x^3+10x^2-4x-8)