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Fractions

Source: 2017 AMC 10B #4, AMC 12B #3

February 16, 2017
AMC 10 BAMC 12 B2017 AMC 10B2017 AMC 12BAMCalgebra

Problem Statement

Suppose that xx and yy are nonzero real numbers such that 3x+yx−3y=−2.\frac{3x+y}{x-3y}= -2. What is the value of x+3y3x−y?\frac{x+3y}{3x-y}?
<spanclass=′latex−bold′>(A)</span>−3<spanclass=′latex−bold′>(B)</span>−1<spanclass=′latex−bold′>(C)</span>1<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A) </span> {-3} \qquad <span class='latex-bold'>(B) </span> {-1} \qquad <span class='latex-bold'>(C) </span> 1 \qquad <span class='latex-bold'>(D) </span>2 \qquad <span class='latex-bold'>(E) </span> 3
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