What is expand (12x(-2x^3+1))/((x^3+1)^3) ?

The solution to expand (12x(-2x^3+1))/((x^3+1)^3) is (-24x^4+12x)/(x^9+3x^6+3x^3+1)

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expand (12x(-2x^3+1))/((x^3+1)^3)

expand

\frac{12 x ( - 2 x ^{3} + 1 )}{( x ^{3} + 1 ) ^{3}}

\frac{- 24 x ^{4} + 12 x}{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}

Solution steps

\frac{12 x ( - 2 x ^{3} + 1 )}{( x ^{3} + 1 ) ^{3}}

(x^{3} + 1)^{3} = x^{9} + 3 x^{6} + 3 x^{3} + 1

= \frac{12 x ( - 2 x ^{3} + 1 )}{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}

Expand

12 x (- 2 x^{3} + 1) : - 24 x^{4} + 12 x

= \frac{- 24 x ^{4} + 12 x}{x ^{9} + 3 x ^{6} + 3 x ^{3} + 1}

(3 - 4 - x)^{2}

(T - a) (T - b) (T - d) (T - e) (T - f)

(2 x^{2} - 5 x + 6) l e f t (3 x^{4} - 5 x^{3} - 6 x^{2} + 4 x - 3)

\frac{2 s}{( s ^{2} + 36 ) ( s - 1 )}

\frac{d}{d t} ((w (t, x (w, t), y (w, t), z (w, t))) (x (w, t)^{2} + y (w, t)^{2} + z (w, t)^{2}))

What is expand (12x(-2x^3+1))/((x^3+1)^3) ?
The solution to expand (12x(-2x^3+1))/((x^3+1)^3) is (-24x^4+12x)/(x^9+3x^6+3x^3+1)