Solve the inequality (x^2 - 6x + 8) / (x - 3) > 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
B. (2, 3) ∪ (4, ∞)
Principle or equation
For a rational inequality, find critical points (zeros of numerator and denominator), test intervals, and exclude points where denominator is zero.
Why this answer is correct
Factor numerator: (x-2)(x-4). Critical points: 2, 3, 4. Test intervals: (-∞,2): positive? (x=0 gives 8/(-3)0. (3,4): x=3.5 gives (1.5*-0.5)/0.5=-1.50. So solution (2,3)∪(4,∞).
Example
Solve (x-1)(x-3)/(x-2)>0: critical 1,2,3; solution (1,2)∪(3,∞).
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