Question

Question #48244

Answer 1

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: `(x-2)/(x+4)=(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.
Solve the resulting quadratics.

`(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:

`4x=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 larr` the answer

check:

`(8-2)/(8+4)=(8+2)/(8+12)`

`6/12=10/20`

`1/2 = 1/2`

This checks.