Solve the inequality (x^2 - 2x - 3) / (x + 4) < 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
A. (-∞, -4) ∪ (-1, 3)
Principle or equation
For a rational inequality, find critical points where numerator or denominator is zero, then test intervals.
Why this answer is correct
Numerator factors as (x - 3)(x + 1). Critical points: x = -4, -1, 3. Test intervals: (-∞,-4): choose -5: (-)(-)/(-) = - (negative). (-4,-1): choose -2: (-)(-)/(+) = +. (-1,3): choose 0: (-)(+)/(+) = -. (3,∞): choose 4: (+)(+)/(+) = +. The inequality is <0, so intervals where negative: (-∞,-4) and (-1,3).
Example
For (x^2 - 1)/(x - 2) < 0, critical points -1,1,2; solution (-∞,-1) ∪ (1,2).
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