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

x + y

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\frac{x y}{x + y}

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x y

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\frac{1}{x y}

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Solution

The correct option is B $\frac{x y}{x + y}$
The value of $(x^{- 1} + y^{- 1})^{- 1}$ is
$= \frac{1}{x^{- 1} + y^{- 1}} = \frac{1}{\frac{1}{x} + \frac{1}{y}} = \frac{1}{\frac{x + y}{x y}} = \frac{x y}{x + y}$
Hence, option (B) is correct.

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