1958 AHSME Problems/Problem 2

Problem

If $\frac {1}{x} - \frac {1}{y} = \frac {1}{z}$ , then $z$ equals:

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

Solution

$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$

$\frac{y}{xy}-\frac{x}{xy}=\frac{1}{z}$

$\frac{y-x}{xy}=\frac{1}{z}$

$\frac{1}{\frac{y-x}{xy}}=\frac{1}{\frac{1}{z}}$

$\frac{xy}{y-x}=z$

The answer is therefore $\boxed{\text{D}}$ .

1958 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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1958 AHSME Problems/Problem 2

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