1952 AHSME Problems/Problem 7

Problem

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

$\textbf{(A) \ }x+y \qquad \textbf{(B) \ }\frac{xy}{x+y} \qquad \textbf{(C) \ }xy \qquad \textbf{(D) \ }\frac{1}{xy} \qquad \textbf{(E) \ }\frac{x+y}{xy}$

Solution

$(x^{-1}+y^{-1})^{-1}=\left(\frac{1}{x}+\frac{1}{y}\right)^{-1}=\left(\frac{x+y}{xy}\right)^{-1}=\boxed{\textbf{(B)}\ \frac{xy}{x+y}}$ .

1952 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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1952 AHSME Problems/Problem 7

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