Official Guide Explanation:
Problem Solving #133




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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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