Solve the inequality (x - 1)/(x + 4) > 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -4) ∪ (1, ∞)
Principle or equation
For a rational inequality, find critical points where numerator or denominator is zero. Test intervals between critical points. The inequality is strict, so endpoints are excluded.
Why this answer is correct
Critical points: x = 1 (numerator zero) and x = -4 (denominator zero). These divide the number line into (-∞, -4), (-4, 1), (1, ∞). Test x = -5: (-6)/(-1)=6>0, so (-∞, -4) works. Test x = 0: (-1)/(4)0, so (1,∞) works. Since inequality is strict, endpoints are not included.
Example
For (x-2)/(x+3) > 0, solution is (-∞,-3) ∪ (2,∞).
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