Solve the inequality (x^2 - 4x - 5) / (x - 2) < 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -1) ∪ (2, 5)
Principle or equation
For a rational inequality, find critical points from numerator and denominator, then test intervals on a number line.
Why this answer is correct
Factor numerator: (x - 5)(x + 1). Critical points: x = -1, 2, 5. Test intervals: (-∞, -1): negative; (-1, 2): positive; (2, 5): negative; (5, ∞): positive. Since we need < 0, the solution is (-∞, -1) ∪ (2, 5).
Example
For (x - 1)/(x - 3) < 0, critical points 1 and 3; test intervals give (1, 3).
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