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

2 Answers
Jun 19, 2016

Answer:

#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

Answer:

#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#