用换元法解方程3x/x^2-1+x^2-1/ 2x=5/2

令t=x/(x²-1)；则有：
3t+1/(2t)=5/2;
6t²+1-5t=0;
(2t-1)(3t-1)=0;
t=1/2或t=1/3;
∴x/x²-1=1/2;
x²-1-2x=0;
(x-1)²=2;
x-1=±√2;
x=1±√2;
或x/x²-1=1/3;
x²-3x-1=0;
(x-3/2)²=13/4;
x-3/2=±√13/2;
x=(3±√13)/2;
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