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

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

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

simplify

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

\frac{ab}{b - a}

Solution steps

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

Apply exponent rule:

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

(a^{- 1} - b^{- 1})^{- 1} = \frac{1}{a ^{- 1} - b ^{- 1}}

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

Simplify

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

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

Join

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

= \frac{1}{\frac{b - a}{ab}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{ab}{b - a}

- 2 x^{2} + 5 x + 12 = 0

\frac{1}{2} (c - 2) + \frac{1}{4} (2 c + 1) = \frac{5}{4}

- x^{2} + 2 x y - y^{2}

16 x^{4} - y^{4}

\frac{4}{5} x + \frac{6}{5} = - \frac{2}{5}

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