Solve the inequality (x - 1)/(x + 3) < 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-3, 1)
Principle or equation
A rational inequality can be solved by finding critical points where the numerator or denominator is zero, then testing intervals.
Why this answer is correct
Critical points are x = 1 (numerator zero) and x = -3 (denominator zero). These divide the real line into intervals: (-∞, -3), (-3, 1), and (1, ∞). Test a point in each: for x = -4, the expression is (-5)/(-1) = 5 > 0; for x = 0, it is (-1)/(3) = -1/3 < 0; for x = 2, it is (1)/(5) > 0. The inequality is satisfied only on (-3, 1).
Example
Solve (x - 2)/(x + 1) < 0. Critical points: 2 and -1. Testing intervals gives (-1, 2).
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