Simplify:

$(i i)$ $(a + b)^{- 1} . (a^{- 1} + b^{- 1})$

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Solution

Simplifying the given expression Given,

$(a + b)^{- 1} . (a^{- 1} + b^{- 1})$

It can be simplified as :

$(a + b)^{- 1} . (a^{- 1} + b^{- 1}) = \frac{1}{a + b} \times (\frac{1}{a} + \frac{1}{b})$

$[∵ x^{- 1} = \frac{1}{x}]$

$= \frac{1}{a + b} \times \frac{b + a}{a b}$ [Taking LCM]

= $\frac{1}{a + b} \times \frac{a + b}{a b} = \frac{1}{a b}$

Hence, the simplified value is $\frac{1}{a b}$

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