Question #48244

1 Answer
May 8, 2017

Answer:

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.