which expression is equivalent to $\frac{x^{2}+7x + 12}{x^{2}-x - 12}$?\n$\frac{x + 3}{x - 3}$\n$\frac{x +…

which expression is equivalent to $\frac{x^{2}+7x + 12}{x^{2}-x - 12}$?\n$\frac{x + 3}{x - 3}$\n$\frac{x + 4}{x - 4}$\n$\frac{(x + 3)(x + 4)}{(x - 3)(x - 4)}$\n$\frac{(x - 3)(x - 4)}{(x + 3)(x + 4)}$

which expression is equivalent to $\frac{x^{2}+7x + 12}{x^{2}-x - 12}$?\n$\frac{x + 3}{x - 3}$\n$\frac{x + 4}{x - 4}$\n$\frac{(x + 3)(x + 4)}{(x - 3)(x - 4)}$\n$\frac{(x - 3)(x - 4)}{(x + 3)(x + 4)}$

Answer

Answer:

A. $\frac{x + 3}{x-3}$

Explanation:

Step1: Factor the numerator

$x^{2}+7x + 12=(x + 3)(x+4)$

Step2: Factor the denominator

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

Step3: Simplify the fraction

$\frac{x^{2}+7x + 12}{x^{2}-x - 12}=\frac{(x + 3)(x + 4)}{(x - 4)(x+3)}=\frac{x + 3}{x-3}$ (cancel out $x + 3$ when $x\neq - 3$)