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}

121 x^{2} - 36 y^{2}

- 2 x^{2} + 5 x - 3

\frac{1}{- 5}

2 x^{3} - 2 v^{4} x^{3}

- 4 y + 5 + 6 y = - 19

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