What is expand (24x(-x^2+1))/((x^2+1)^4) ?

The solution to expand (24x(-x^2+1))/((x^2+1)^4) is (-24x^3+24x)/(x^8+4x^6+6x^4+4x^2+1)

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expand (24x(-x^2+1))/((x^2+1)^4)

expand

\frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

\frac{- 24 x ^{3} + 24 x}{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1}

Solution steps

\frac{24 x ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{4}}

(x^{2} + 1)^{4} = x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 1

= \frac{24 x ( - x ^{2} + 1 )}{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1}

Expand

24 x (- x^{2} + 1) : - 24 x^{3} + 24 x

= \frac{- 24 x ^{3} + 24 x}{x ^{8} + 4 x ^{6} + 6 x ^{4} + 4 x ^{2} + 1}

\frac{\partial}{\partial y} ((z) (yz + x ln (y)))

e^{x} (x^{3} - \frac{486 x}{5}) + e^{x} (3 x^{2} - \frac{486}{5})

(z^{2} - 2 z + 1)^{8}

\frac{πj}{z ( z - π - πj ) ( z + π + πj )}

cos (x) \cdot (1 + \frac{tan ^{2} ( x )}{sec ( x ) + 1})

What is expand (24x(-x^2+1))/((x^2+1)^4) ?
The solution to expand (24x(-x^2+1))/((x^2+1)^4) is (-24x^3+24x)/(x^8+4x^6+6x^4+4x^2+1)