Solve the inequality (x^2 - 4x - 5) / (x - 3) > 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-1, 3) ∪ (5, ∞)
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-5)(x+1). Critical points: x = -1, 3, 5. Test intervals: (-∞,-1): choose -2, (-)(-)/(-) = -; (-1,3): choose 0, (-)(+)/(-) = +; (3,5): choose 4, (-)(+)/(+) = -; (5,∞): choose 6, (+)(+)/(+) = +. So solution is (-1,3) ∪ (5,∞).
Example
Solve (x-1)/(x+2) > 0: critical points -2,1; test intervals gives (-∞,-2) ∪ (1,∞).
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