Solve the inequality (2x - 3)/(x + 1) > 1. Which of the following is the solution set?
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Correct answer
A. (-∞, -1) ∪ (4, ∞)
Principle or equation
For rational inequalities, bring all terms to one side, combine into a single fraction, find critical points, and test intervals.
Why this answer is correct
Subtract 1: (2x - 3)/(x + 1) - 1 > 0 => (2x - 3 - x - 1)/(x + 1) > 0 => (x - 4)/(x + 1) > 0. Critical points: x = 4 and x = -1. Test intervals: (-∞, -1): (-)/(-) = +, so true; (-1, 4): (-)/(+) = -, false; (4, ∞): (+)/(+) = +, true. Solution: (-∞, -1) ∪ (4, ∞).
Example
Solve (x - 2)/(x + 3) > 0: critical points -3 and 2; solution (-∞, -3) ∪ (2, ∞).
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