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

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

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

expand

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

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

Solution steps

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

(x^{2} + 1)^{3} = x^{6} + 3 x^{4} + 3 x^{2} + 1

= \frac{2 x ( - x ^{2} + 3 )}{x ^{6} + 3 x ^{4} + 3 x ^{2} + 1}

Expand

2 x (- x^{2} + 3) : - 2 x^{3} + 6 x

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

(2 sin (x) - 4)^{2}

(4 + x) x^{3} e^{4 x} + 5

\frac{( x - 1 ) ( y - 1 ) ( z - 1 )}{( a - 1 ) ( b - 1 )}

\frac{( - 3 - i ) ^{\frac{1}{3}} - 1}{3}

(m n^{3} + \frac{1}{4}) (m n^{3} - \frac{1}{5})

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