# How do you solve #(x - 2)/( x + 1) =( x + 1)/(x - 2)#?

##### 2 Answers

#### Explanation:

Cross multiply the terms,

If both x-2 and x+1 are positive or negative, then this has no solution.

If x+1 is negative, then x-2 is also negative. (

So our only option is if x-2 is negative and x+1 is positive.

In this case,

We have,

#### Explanation:

Given:

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

Multiply both sides by

#(x-2)^2 = (x+1)^2#

Expanding both sides this becomes:

#x^2-4x+4 = x^2+2x+1#

Subtract

#-4x+4 = 2x+1#

Add

#4 = 6x+1#

Subtract

#3 = 6x#

Divide both sides by

#x = 1/2#