# Question 48244

May 8, 2017

Restrict the values of x to prevent division by 0.
Multiply both sides by the product of the denominators.
Solve the resulting equation.

#### Explanation:

Given: $\frac{x - 2}{x + 4} = \frac{x + 2}{x + 12}$

Restrict the values of x to prevent division by 0.

(x-2)/(x+4)=(x+2)/(x+12); x!=-4, x!=-12

Multiply both sides by the product of the denominators.

(x-2)(x+12)=(x+2)(x+4); x!=-4, x!=-12

x^2+10x-24 = x^2 + 6x+8; x!=-4, x!=-12#

Combine like terms:

$4 x = 32$

Please notice that I have dropped the restrictions, because the solution is not going to be either of them.

Divide both sides by 4:

$x = 8 \leftarrow$ the answer

check:

$\frac{8 - 2}{8 + 4} = \frac{8 + 2}{8 + 12}$

$\frac{6}{12} = \frac{10}{20}$

$\frac{1}{2} = \frac{1}{2}$

This checks.