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

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

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

expand

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

\frac{- 2 t ^{2} + 2}{t ^{4} + 2 t ^{2} + 1}

Solution steps

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

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

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

Expand

2 (- t^{2} + 1) : - 2 t^{2} + 2

= \frac{- 2 t ^{2} + 2}{t ^{4} + 2 t ^{2} + 1}

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

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

\frac{x ^{2} + 7 x + 11}{( x + 2 ) ( x + 1 ) ( x + 3 )}

e^{(x^{2} + y^{2})^{2}}

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

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