解方程3x/(x²-1)+(x²-1)/3x=5/2

解方程3x/(x²-1)+(x²-1)/3x=5/2
解方程3x/(x²-1)+(x²-1)/3x=5/2

解方程3x/(x²-1)+(x²-1)/3x=5/2
令A=3x/(x²-1)
原式:A+1/A=5/2

2A^2-5A+2=0
(A-2)(2A-1)=0
A=2或A=1/2

A=2
3x=2x^2-2
2x^2-3x-2=0
(x-2)(2x+1)=0
x=2或x=-1/2

A=1/2
x^2-1=6x
x^2-6x-1=0
x=3±√10

综上x=2或x=-1/2或x=3±√10