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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

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

7 (x - 6)

4 (1 - sin (θ))

(x - 6) (7 x + 2)

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