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## Official Guide Explanation:Problem Solving #133

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 133
Page: 79
Difficulty: 5 (Moderate)
Category 1: Algebra > Simplifying Algebraic Expressions >
Category 2: Algebra > Solving Equations by Factoring >

Explanation: Given a particularly knotty - looking fraction, look for ways to simplify. There's an (x - 2) in both the numerator and the denominator, but since (x - 2) can't yet be factored out of the numerator, that doesn't help much. First, recognize that -x + 2= - (x - 2), and rewrite the numerator: 3x2(x - 2) - 1(x - 2), and factor out (x - 2):

(x - 2)(3x2-1)

Now, simplify the fraction:

(((x - 2)(3x2-1))/((x - 2))) = 3x2-1, choice (D).

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