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})
Correct Answer: Option D
Explanation
(frac{2x^2 – 5x – 12}{4x^2 – 9}) = (frac{3x^2 – 8x + 3x – 12}{(2x)^2 – 3^2})
= (frac{32(x – 4) + 3(x – 4)}{(2x – 3)(2x + 3)} – frac{(x – 4) + (2x + 3)}{(2x – 3) (2x + 3)})
= (frac{x – 4}{2x – 3})