Question

question
simplify the expression completely if possible.
$\frac{x^{2}-9}{x^{2}+x-12}$

Explanation:

Step1: Factor numerator (difference of squares)

$x^2 - 9 = (x-3)(x+3)$

Step2: Factor denominator (quadratic trinomial)

$x^2 + x - 12 = (x-3)(x+4)$

Step3: Cancel common factor $(x-3)$

$\frac{(x-3)(x+3)}{(x-3)(x+4)} = \frac{x+3}{x+4}$ (where $x
eq 3, -4$)

Answer:

$\frac{x+3}{x+4}$ (with the restriction $x
eq 3, -4$)