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.

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Solution and Metadata

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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