Solve the inequality (x^2 - 2x - 8) / (x + 3) < 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -4) ∪ (-3, 2)
Principle or equation
For a rational inequality, find critical points where numerator or denominator is zero, then test intervals on the number line.
Why this answer is correct
Factor numerator: x^2 - 2x - 8 = (x - 4)(x + 2). Critical points: x = -2, 4, and x = -3 (denominator zero). Test intervals: (-∞, -4), (-4, -3), (-3, 2), (2, 4), (4, ∞). The inequality is < 0 on (-∞, -4) and (-3, 2).
Example
For (x^2 - 1)/(x - 2) < 0, critical points -1, 1, 2; solution (-∞, -1) ∪ (1, 2).
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