Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.8 Junior Find the answer

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

Pick one

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 $\boxed{\text{D}}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.