State whether the statement is True or False.
$(m + n)^{- 1} (m^{- 1} + n^{- 1}) = (m n)^{- 1}$

True

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False

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Solution

The correct option is A True
L.H.S $= (m + n)^{- 1} (m^{- 1} + n^{- 1})$
$= \frac{1}{m + n} (\frac{1}{m} + \frac{1}{n})$
$= \frac{1}{m + n} (\frac{m + n}{m n})$
$= \frac{1}{m n}$
$= (m n)^{- 1}$
$=$ R.H.S

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