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Difficult Fraction

Source: AHSME 1963 Problem 17

January 9, 2014
algebrafunctiondomainAMC

Problem Statement

The expression aa+y+ya−yya+y−aa−y\dfrac{\dfrac{a}{a+y}+\dfrac{y}{a-y}}{\dfrac{y}{a+y}-\dfrac{a}{a-y}}, a real, a≠0a\neq 0, has the value −1-1 for:
<spanclass=′latex−bold′>(A)</span> all but two real values of y<spanclass=′latex−bold′>(B)</span> only two real values of y<span class='latex-bold'>(A)</span>\ \text{all but two real values of }y \qquad <span class='latex-bold'>(B)</span>\ \text{only two real values of }y \qquad
<spanclass=′latex−bold′>(C)</span> all real values of y<spanclass=′latex−bold′>(D)</span> only one real value of y<spanclass=′latex−bold′>(E)</span> no real values of y<span class='latex-bold'>(C)</span>\ \text{all real values of }y \qquad <span class='latex-bold'>(D)</span>\ \text{only one real value of }y \qquad <span class='latex-bold'>(E)</span>\ \text{no real values of }y
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