Simplify and express the expression $(x + y)^{- 1} (x^{- 1} + y^{- 1})$ with negative exponents

x^{- 2} + 2 x^{- 1} y^{- 1} + y^{- 2}

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x^{- 2} + 2^{- 1} x^{- 1} y^{- 1} + y^{- 2}

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x^{- 1} y^{- 1}

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x^{- 2} + y^{- 2}

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Solution

The correct option is D $x^{- 1} y^{- 1}$
${(x + y)}^{- 1} (x^{- 1} + y^{- 1}) = \frac{1}{(x + y)} [\frac{1}{x} + \frac{1}{y}]$
$= \frac{1}{(x + y)} [\frac{y + x}{x y}]$
$= \frac{1}{x y}$
$= x^{- 1} y^{- 1}$

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