For all nonzero real numbers x and y such that x-y=xy, 1x-1y equals

1979 AMC 12 Problem 2

Attempt Problem 2 of the 1979 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1979 AMC 12 solutions, or check the answer key.

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For all nonzero real numbers

x

and

y

such that

x-y=xy,

\frac1x-\frac1y

equals

\frac1{xy}

\frac1{x-y}

0

-1

y-x

Combine the two reciprocals over the denominator

xy

Use the given equation to replace

y-x

We have

\begin{aligned} \frac1x-\frac1y&=\frac{y-x}{xy}\\ &=-\frac{x-y}{xy}\\ &=-1, \end{aligned}

because

x-y=xy.

Therefore, the correct answer is D.