Source: Extra Practice
Find the solution set of the inequality: (x - 2) / (x + 5) > 0
Options
Option A
(-5, 2)
Option B is correct
(-∞, -5) ∪ (2, ∞)
Option C
[-5, 2]
Option D
(-∞, -5] ∪ [2, ∞)
Explanation
The critical points are x = 2 and x = -5. These points divide the number line into three intervals: (-∞, -5), (-5, 2), and (2, ∞). Testing a point in each: for x=3, (3-2)/(3+5) = 1/8 > 0 (Positive); for x=0, (0-2)/(0+5) = -2/5 0 (Positive). Since the inequality is strictly greater than 0, we exclude endpoints where the expression is zero or undefined. Thus, the solution is (-∞, -5) ∪ (2, ∞). Option 1 is the region where it is negative. Options 3 and 4 incorrectly include endpoints.