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1978 AMC 12 Question 3

AMC12 · 1978 AMC 12

Question 3

For all nonzero numbers $x$ and $y$ such that $x=\frac{1}{y},$ $$
\left(x-\frac1x\right)\left(y+\frac1y\right)
$$ equals
  1. $2x^2$
  2. $2y^2$
  3. $x^2+y^2$
  4. $x^2-y^2$
  5. $y^2-x^2$