Prove that : $(m + n)^{- 1} (m^{- 1} + n^{- 1}) = (m n)^{- 1}$

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Solution

$L.H.S. (m + n)^{- 1} (m^{- 1} + n^{- 1}) = \frac{1}{m + n} (\frac{1}{m} + \frac{1}{n}) = \frac{1}{m + n} . \frac{n + m}{m n} = \frac{1}{m n} = (m n)^{- 1} = R.H.S.$

Hence proved.

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