x+1/x-1 + x-1/x+1=5/2

(x+1)/(x-1)+(x-1)/(x+1)=5/2
(x²+2x+1+x²-2x+1)/(x²-1)=5/2
2(2x²+2)=5(x²-1)
4x²+4=5x²-5
5x²-4x²=4+5
x²=9
x=-3
x=3