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

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

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

expand

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

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

Solution steps

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

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

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

Expand

(1 - x) (1 + 2 x^{2} + x^{4}) : 1 + 2 x^{2} + x^{4} - x - 2 x^{3} - x^{5}

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

sin (x) (1 + cos (x))

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

tan (x) (1 - cot^{2} (x)) + cot (x) (1 - tan^{2} (x))

(x + i y)^{6}

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