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

Question

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

Answer 1

(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

Answer 2

   
 ОДЗ: х не равен -1 и 1
2(x+1)²+2(x-1)²=5(x-1)(x+1)
2x²+4x+2+2x²-4x+2=5x²-5
x²=9
x=3 и х=-3