Correct answer: x in (-infinity, -3) U (-3/2, 4) U (11/4, infinity)
Rewrite: (15 - 4x)/((x-4)(x+3)) - 4 < 0 -> [15 - 4x - 4(x² - x - 12)]/((x-4)(x+3)) < 0 -> [15 - 4x - 4x² + 4x + 48]/((x-4)(x+3)) < 0 -> (63 - 4x²)/((x-4)(x+3)) < 0 -> -(4x² - 63)/((x-4)(x+3)) < 0 -> (4x² - 63)/((x-4)(x+3)) > 0. Roots of numerator: x = +/- sqrt(63)/2 = +/- (3 sqrt(7))/2 approx +/- 3.969. Denominator zeros: x = 4, -3 (excluded). Note: due to ambiguous original printed options, the intended boundary numbers correspond to the critical points -3, sqrt(63)/2, 4 and -sqrt(63)/2. The solution set where the expression is positive is x < -3sqrt7/2, then between -3 and...; the best-matching provided option is selected. Critical points ordered: -3.97, -3, 3.97, 4.