What is (a-b)/(a^{-1)-b^{-1}} ?

The solution to (a-b)/(a^{-1)-b^{-1}} is -ab

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simplify (a-b)/(a^{-1)-b^{-1}}

simplify

\frac{a - b}{a ^{- 1} - b ^{- 1}}

- ab

Solution steps

\frac{a - b}{a ^{- 1} - b ^{- 1}}

Simplify

a^{- 1} - b^{- 1} : \frac{b - a}{ab}

= \frac{a - b}{\frac{b - a}{ab}}

Apply the fraction rule:

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

= \frac{( a - b ) ab}{b - a}

Cancel

\frac{( a - b ) ab}{b - a} : - ab

= - ab

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