# How do you solve #(2(x-2))/(x^2-10x+16)=2/(x+2)#?

##### 2 Answers

(no solutions)

#### Explanation:

First, let's factor

We need two factors of 16 which add up to -10.

#-2 and -8# work, so our factored polynomial is:

#(x-2)(x-8)#

Now we can solve the equation:

#(2(x-2))/(x^2-10x+16)=2/(x+2)#

#(2(x-2))/((x-2)(x-8)) = 2/(x+2)#

#(color(blue)cancel(color(black)2)color(red)cancel(color(black)((x-2))))/(color(red)cancel(color(black)((x-2)))(x-8)) = color(blue)cancel(color(black)2)/(x+2)#

#1/(x-8) = 1/(x+2)#

Now take the reciprocal of both sides:

#x-8 = x+2#

#-8 = 2#

This is impossible, so there are no solutions.

No solution

#### Explanation:

multiply both sides by (x-8)(x+2)

No solution