L.H.S (m+n)^ 1(m^ 1+n^ 1) =1m+n(1m+1n) =1m+n×n+mmn=1mn =(mn)^ 1 =R.H.S.Hence proved. ...

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Question

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

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Solution

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

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