Question

Which expression is equivalent to x^2+7x+12/x^2-x-12?

Answer 1

X^2+7x+12/x^2-x-12
x^2+4x+3x+12/x^2+3x-4x-12
x * (x+4) +3(x+4)/ x* (x+3)-4(x+3)
(x+3)(x+4)/(x-4)(x+3)

x+4/x-4

Answer 2

Answer:

$\frac{(x+4)}{(x-4)}$

Step-by-step explanation:

Given : $\frac{x^2+7x+12}{x^2-x-12}$

Solution:

$\frac{x^2+7x+12}{x^2-x-12}$

Factorize the numerator and denominator.

$\frac{x^2+3x+4x+12}{x^2-4x+3x-12}$

$\frac{x(x+3)+4(x+3)}{x(x-4)+3(x-4)}$

$\frac{(x+4)(x+3)}{(x-4)(x+3)}$

$\frac{(x+4)}{(x-4)}$

So, $\frac{x^2+7x+12}{x^2-x-12}$ =  $\frac{(x+4)}{(x-4)}$

Hence Option B is correct.