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

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

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

expand

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

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

Solution steps

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

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

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

e^{2 x} (cos (x) - sin (x))

\frac{d ^{4}}{d x ^{4}} ((y) (\frac{3}{x ^{2}} - \frac{x ^{2}}{3}))

(1 - e^{- 2 x}) d x

\frac{( x ^{2} - 5 ) ^{3}}{125}

4 sin (\frac{π}{2} (x - 3)) + 8

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