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Expression is equivalent to...

Source: 1964 AHSME Problem 4

September 12, 2012
AMC

Problem Statement

The expression
P+QP−Q−P−QP+Q \frac{P+Q}{P-Q}-\frac{P-Q}{P+Q}
where P=x+yP=x+y and Q=x−yQ=x-y, is equivalent to:
<spanclass=′latex−bold′>(A)</span> x2−y2xy<spanclass=′latex−bold′>(B)</span> x2−y22xy<spanclass=′latex−bold′>(C)</span> 1<spanclass=′latex−bold′>(D)</span> x2+y2xy<spanclass=′latex−bold′>(E)</span> x2+y22xy{ <span class='latex-bold'>(A)</span>\ \frac{x^2-y^2}{xy}\qquad<span class='latex-bold'>(B)</span>\ \frac{x^2-y^2}{2xy}\qquad<span class='latex-bold'>(C)</span>\ 1 \qquad<span class='latex-bold'>(D)</span>\ \frac{x^2+y^2}{xy} \qquad<span class='latex-bold'>(E)</span>\ \frac{x^2+y^2}{2xy} }
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