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Question

If $\frac{1}{x} - \frac{1}{y} = \frac{1}{z}$ , then $z$ is equal to

$x - y$
$\frac{y - x}{x y}$
$y - x$
$\frac{x y}{y - x}$
$\frac{x y}{x - y}$

A

x - y

B

\frac{y - x}{x y}

C

\frac{x y}{y - x}

D

y - x

E

\frac{x y}{x - y}

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Solution

Verified by Toppr

The correct option is D $\frac{x y}{y - x}$
If $\frac{1}{x} - \frac{1}{y} = \frac{1}{z}$

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

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

option D is correct

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