Simplify the expression to lowest terms. 4x^2 - 9/2x^2+11x+12

(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)

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