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UKMT Senior Mathematical Challenge, 2009

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Suppose that $x - \frac{1}{x} = y - \frac{1}{y}$ and $x \neq y$ . What is the value of $xy$ ?

(A) $4$ (B) $1$ (C) $-1$ (D) $-4$ (E) more information is needed

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