Official Guide Explanation:
Problem Solving #208

Background

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Solution and Metadata

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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