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 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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1958 AHSME Problems/Problem 2

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