Question

simplify the numerator of the rational function.
$f(x) = \frac{6x^2+30x+36}{x^2-4}$
$(x + 3)(x + 4)$
$(x + 7)(x + 3)$
$(x + 4)(x + 6)$
$(x + 2)(x - 2)$

Explanation:

Step1: Identify numerator polynomial

The numerator is $x^2 - 4$.

Step2: Factor the difference of squares

Use $a^2-b^2=(a-b)(a+b)$. Here $a=x$, $b=2$.
$x^2 - 4 = (x-2)(x+2)$

Answer:

$(x + 2)(x - 2)$ (Option corresponding to this factorization)