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## Official Guide Explanation:Problem Solving #208

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 208
Page: 182
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Arithmetic > Fractions >

Explanation: Start by writing the expression with (1/(x)) replacing x: ((((1/(x)) + 1)/((1/(x)) - 1)))2. To simplify, multiply the top and bottom of the fraction by x:

(((x((1/(x)) + 1))/(x((1/(x)) - 1))))2 = (((1 + x)/(1 - x)))2. This looks very similar to (A), as x + 1 = 1 + x, but since 1 - x ≠ x - 1, it looks like a problem. However, the expressions are the same: 1 - x has the same absolute value as x - 1, the two expressions just don't have the same sign. Since ( ((1 + x)/(1 - x)))2 is squared, it doesn't matter: both results are positive, so (A) is correct.

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