Simplify: \(\frac{2x^2 – 5x – 12}{4x^2 – 9}\)
- \(\frac{x + 4}{2x + 3}\)
- \(\frac{x + 4}{2x - 3}\)
- \(\frac{x - 4}{2x + 3}\)
-
\(\frac{x - 4}{2x - 3}\)
The correct answer is: D
Explanation
\(\frac{2x^2 - 5x - 12}{4x^2 - 9}\) = \(\frac{2x^2 - 8x + 3x - 12}{(2x)^2 - 3^2}\)
= \(\frac{2x(x - 4) + 3(x - 4)}{(2x - 3)(2x + 3)} - \frac{(x - 4) + (2x + 3)}{(2x - 3) (2x + 3)}\)
= \(\frac{x - 4}{2x - 3}\)