Answer:
(2x - 3)/(x +4)
Step-by-step explanation:
Given the expression 4x^2 - 9/2x^2+11x+12
Simplify the numerator
4x^2 - 9 = (2x)^2 - 3^2
Recall that a^2 - b^2 = (a-b)(a+b)
Hence 4x^2 - 9 = (2x - 3)(2x + 3)
The denominator
2x^2+11x+12
Factorize
2x^2+11x+12 = 2x^2+8x + 3x+12
=2x(x + 4) + 3(x + 4)
= (2x + 3)(x + 4)
Hence
4x^2 - 9/2x^2+11x+12 = (2x - 3)(2x + 3)/(2x + 3)(x + 4)
= (2x - 3)/(x +4)
