What is expand (-4x^3+1)/(2x^{1/2)(x^3+1)^2} ?

The solution to expand (-4x^3+1)/(2x^{1/2)(x^3+1)^2} is (-4x^3+1)/(2x^{13/2)+4x^{7/2}+2x^{1/2}}

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expand (-4x^3+1)/(2x^{1/2)(x^3+1)^2}

expand

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

\frac{- 4 x ^{3} + 1}{2 x ^{\frac{13}{2}} + 4 x ^{\frac{7}{2}} + 2 x ^{\frac{1}{2}}}

Solution steps

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

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

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

Expand

2 x^{\frac{1}{2}} (x^{6} + 2 x^{3} + 1) : 2 x^{\frac{13}{2}} + 4 x^{\frac{7}{2}} + 2 x^{\frac{1}{2}}

= \frac{- 4 x ^{3} + 1}{2 x ^{\frac{13}{2}} + 4 x ^{\frac{7}{2}} + 2 x ^{\frac{1}{2}}}

(x + 3) (x + 1) (0.2 x) (\frac{1}{2})

(2 x^{3} + 9 x^{2} + 3 x - 4) d i v i d e (x + 4)

\frac{d}{d x} ((f (x, y)) f (x, y) (x^{3} - 3 x y + y^{2}))

\frac{\partial}{\partial t} ((x) (x^{2} + y^{2}))

\frac{K}{x ( 1 - x T )}

What is expand (-4x^3+1)/(2x^{1/2)(x^3+1)^2} ?
The solution to expand (-4x^3+1)/(2x^{1/2)(x^3+1)^2} is (-4x^3+1)/(2x^{13/2)+4x^{7/2}+2x^{1/2}}