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Question

Prove that:
$(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

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Solution

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

So, $(a^{- 1} + b^{- 1})^{- 1} = \frac{a b}{a + b}$

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