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

The solution to expand 1/((x-1)^3(x^2+x+1)^2) is 1/(x^7-x^6-2x^4+2x^3+x-1)

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

expand

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

\frac{1}{x ^{7} - x ^{6} - 2 x ^{4} + 2 x ^{3} + x - 1}

Solution steps

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

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

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

(x^{2} + x + 1)^{2} = x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1

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

Expand

(x^{3} - 3 x^{2} + 3 x - 1) (x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1) : x^{7} - x^{6} - 2 x^{4} + 2 x^{3} + x - 1

= \frac{1}{x ^{7} - x ^{6} - 2 x ^{4} + 2 x ^{3} + x - 1}

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

tan (\frac{β}{2}) \cdot (1 + cos (β))

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

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

What is expand 1/((x-1)^3(x^2+x+1)^2) ?
The solution to expand 1/((x-1)^3(x^2+x+1)^2) is 1/(x^7-x^6-2x^4+2x^3+x-1)