When simplified ${(x^{- 1} + y^{- 1})}^{- 1}$ is equal to--

x y

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x + y

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\frac{x y}{x + y}

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\frac{x + y}{x y}

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Solution

The correct option is C $\frac{x y}{x + y}$
Given Exp. = ${(x^{- 1} + y^{- 1})}^{- 1}$
$= \frac{1}{(x^{- 1} + y^{- 1})}$
= $\frac{1}{(\frac{1}{x} + \frac{1}{y})}$
= $\frac{1}{(\frac{y + x}{x y})}$
= $\frac{x y}{(x + y)}$

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