令a=x/(x²-1)
则3a+1/a=7/2
6a²-7a+2=0
(2a-1)(3a-2)=0
a=1/2,a=2/3
x/(x²-1)=1/2
x²-x-1=0
x=(1±√5)/2
x/(x²-1)=2/3
2x²-3x-2=0
(2x+1)(x-2)=0
x=-1/2,x=2
所以
x=(1-√5)/2,x=(1+√5)/2,x=-1/2,x=2