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1967 AMC 12 Question 2

AMC12 · 1967 AMC 12

Question 2

An equivalent of the expression

$$
\begin{aligned} &\left(\frac{x^2+1}{x}\right) \left(\frac{y^2+1}{y}\right)\\ &\quad+ \left(\frac{x^2-1}{y}\right) \left(\frac{y^2-1}{x}\right),\\ &\qquad xy\ne0, \end{aligned}
$$

is:
  1. $1$
  2. $2xy$
  3. $2x^2y^2+2$
  4. $2xy+\dfrac{2}{xy}$
  5. $\dfrac{2x}{y}+\dfrac{2y}{x}$