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Popular >

simplify (x^{-1}-1)/(x-1)

Solution

simplify

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

Solution

- \frac{1}{x}

Solution steps

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

Simplify

x^{- 1} - 1 : \frac{- x + 1}{x}

= \frac{\frac{- x + 1}{x}}{x - 1}

Apply the fraction rule:

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

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

Cancel

\frac{- x + 1}{x ( x - 1 )} : - \frac{1}{x}

= - \frac{1}{x}

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Frequently Asked Questions (FAQ)

What is (x^{-1}-1)/(x-1) ?
The solution to (x^{-1}-1)/(x-1) is -1/x