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

2 Answers
Jun 19, 2016

x=1/2

Explanation:

Cross multiply the terms,

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

|x-2| = |x+1|

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. (x+1<0 means x<-1 which means maximum value of x-2 is less than -1-2=-3 which is also negative)

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

In this case, |x-2| = 2-x and |x+1| = x+1

We have,

2-x = x+1

2x=1

x=1/2

Jun 19, 2016

x = 1/2

Explanation:

Given:

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

Multiply both sides by (x+1)(x-2) to get:

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

Expanding both sides this becomes:

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

Subtract x^2 from both sides to get:

-4x+4 = 2x+1

Add 4x to both sides to get:

4 = 6x+1

Subtract 1 from both sides to get:

3 = 6x

Divide both sides by 6 and transpose to get:

x = 1/2