Solve the inequality (x - 3)/(x + 2) < 0. Which of the following is the solution set?

Correct answer

A. (-2, 3)

Principle or equation

For a rational inequality of the form (x - a)/(x - b) < 0, the sign changes at the critical points a and b (where numerator or denominator is zero). The solution is the interval where the expression is negative, excluding points where denominator is zero.

Why this answer is correct

Critical points are x = 3 (numerator zero) and x = -2 (denominator zero). Test intervals: For x < -2, both numerator and denominator are negative, so fraction positive. For -2 < x < 3, numerator negative, denominator positive, so fraction negative. For x > 3, both positive, so fraction positive. Thus the inequality holds for -2 < x < 3, i.e., (-2, 3). Note x = -2 is excluded because denominator cannot be zero.

Example

For (x - 1)/(x + 1) < 0, critical points 1 and -1; test gives solution (-1, 1).