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

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

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

expand

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

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

Solution steps

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

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

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

x^{10} (- 2 e^{- 2 x} + 3 e^{- 3 x})

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

(2 n + 1) sin (\frac{π}{3 ^{n}})

e^{3 x} Q + 3 e^{3 x} (P + Q x)

3 (x^{2} + y^{2}) d x + 7 x y d y

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