To solve (x - 1) / (x + 2) > 0, we identify the critical points where the numerator or denominator is zero, which are x = 1 and x = -2. These points divide the number line into three intervals: (-∞, -2), (-2, 1), and (1, ∞). Testing a value in each: for x = -3, (-4)/(-1) = 4 > 0 (True); for x = 0, (-1)/(2) = -0.5 0 (True). Since the inequality is strict (>), we exclude the endpoints. Thus, the solution is (-∞, -2) ∪ (1, ∞).