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

1 Answer
Sep 25, 2016

Answer:

#x=-4#

Explanation:

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

Multiply the given equation through by #x^2-1 = (x-1)(x+1)# to get:

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

Multiply out to get:

#2x-2+x^2+x = 2#

Simplify to get:

#x^2+3x-2 = 2#

Subtract #2# from both sides and transpose to get:

#0 = x^2+3x-4 = (x+4)(x-1)#

From this we find #x=1# or #x=-4#

Note that #x=1# is a solution of the derived equation, but is not a solution of the original equation since it causes two of the denominators to be #0#.

So the only valid solution is #x=-4#