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

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

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

simplify

\frac{x}{x ^{2} - x}

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

Solution steps

\frac{x}{x ^{2} - x}

Multiply by the conjugate

\frac{x ^{2} - x}{x ^{2} - x}

= \frac{x x ^{2} - x}{x ^{2} - x x ^{2} - x}

x^{2} - x x^{2} - x = x^{2} - x

= \frac{x x ^{2} - x}{x ^{2} - x}

Factor

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

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

Cancel the common factor:

x

= \frac{x ^{2} - x}{x - 1}

\frac{4}{4 ^{3}}

- \frac{2}{7} - \frac{10}{11}

x x^{3}

(s^{- 2} t^{2})^{2} (s^{2} t)^{3}

What is x/(sqrt(x^2-x)) ?
The solution to x/(sqrt(x^2-x)) is (sqrt(x^2-x))/(x-1)