What is x/((x-1)^2)-x ?

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

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simplify x/((x-1)^2)-x

simplify

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

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

Solution steps

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

Apply the fraction rule:

a + \frac{b}{c} = \frac{a c + b}{c}

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

Simplify

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

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

(a + b)^{3} - (a - b)^{3}

\frac{x ^{p^{2}}}{x ^{q^{2}}}

\frac{18}{- 2}

125 t^{3} + d^{3}

\frac{18}{28}