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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

\frac{( tan ( x ) + sin ( x ) ) cos ( x )}{csc ( x ) + cot ( x )}

\frac{n !}{n ( n - 1 )}

\frac{d}{d t} ((x (t, r)) (r (t - sin (t))))

\frac{d ^{2}}{d x ^{2}} ((y) (cos (π x y) - \frac{1}{x} + \frac{2}{y ^{3}}))

sin (x) (1 + tan (x)) + cos (x) (1 + cot (x))

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