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Reciprocal of (1-x)

Source: 1976 AHSME Problem 1

May 14, 2014
AMC

Problem Statement

If one minus the reciprocal of (1−x)(1-x) equals the reciprocal of (1−x)(1-x), then xx equals
<spanclass=′latex−bold′>(A)</span>−2<spanclass=′latex−bold′>(B)</span>−1<spanclass=′latex−bold′>(C)</span>1/2<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A) </span>-2\qquad<span class='latex-bold'>(B) </span>-1\qquad<span class='latex-bold'>(C) </span>1/2\qquad<span class='latex-bold'>(D) </span>2\qquad <span class='latex-bold'>(E) </span>3
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