Official Guide Explanation:
Problem Solving #215

Background

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Solution and Metadata

Question: 215
Page: 183
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Linear Equations-One Unk >
Category 2: Algebra > Simplifying Algebraic Expressions >
Category 3: Arithmetic > Fractions >

Explanation: This is an excellent problem on which to guess and check. Because the denominators are x, x + 1, and x + 4, choices (A), (B), and (E) cannot be correct: they would result in zero in a denominator. So, there are really only two possible values of x to plug into the equation and test. Let's try (C):

(1/(-2)) - (1/((-2 + 1))) = (1/((-2 + 4)))

-(1/2) - (1/(-1)) = (1/2)

-(1/2) + 1 = (1/2)

That's right, so (C) must be the correct choice.

Alternatively, this question can be solved algebraically (but it's much more time consuming than the first method).

(1/(x)) - (1/(x + 1)) = (1/(x + 4))

((x + 1)/(x(x + 1))) - ((x)/(x(x + 1))) = (1/(x + 4))

((x + 1 - x)/(x² + x)) = (1/(x + 4))

x + 4 = x² + x

x²-4 = 0

x = \pm 2

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