Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)
A
\(\frac{x + 4}{2x + 3}\)
B
\(\frac{x + 4}{2x - 3}\)
C
\(\frac{x - 4}{2x + 3}\)
D
\(\frac{x - 4}{2x - 3}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{2x^2 - 5x - 12}{4x^2 - 9}\) = \(\frac{2x^2 - 8x + 3x - 12}{(2x)^2 - 3^2}\)
= \(\frac{2x(x - 4) + 3(x - 4)}{(2x - 3)(2x + 3)} - \frac{(x - 4) + (2x + 3)}{(2x - 3) (2x + 3)}\)
= \(\frac{x - 4}{2x - 3}\)
Source: Myschool Past Questions Archive (Record #36355)