What is factor (x-1)^{1/3}-(x^2-x)(x-1)^{-2/3} ?

The solution to factor (x-1)^{1/3}-(x^2-x)(x-1)^{-2/3} is -(x-1)^{4/3}

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factor (x-1)^{1/3}-(x^2-x)(x-1)^{-2/3}

factor

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

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

Solution steps

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

Factor

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

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

Factor out common term

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

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

Simplify

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

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

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What is factor (x-1)^{1/3}-(x^2-x)(x-1)^{-2/3} ?
The solution to factor (x-1)^{1/3}-(x^2-x)(x-1)^{-2/3} is -(x-1)^{4/3}