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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

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

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

(2 x t + 4 x + 3 y) d x + (x^{2} + 3 x) d y

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

6 - x ((- 2 - x) (5 - x))

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