题目有点问题,应是(x²+3x+1)/(4x²+6x-1) - (12x²+18x-3)/(x²+3x+1)=2

(x²+3x+1)/(4x²+6x-1) - 3(4x²+6x-1)/(x²+3x+1)=2
令(x²+3x+1)/(4x²+6x-1)=m
m- 3/m=2
m²-2m-3=0
m=3或-1
(x²+3x+1)/(4x²+6x-1)= 3,化简得： 11x²+15x-4=0,解得x= (-15±√401)/22
(x²+3x+1)/(4x²+6x-1)=-1,化简得： 5x²+9x=0,解得x= 0 或-9/5
经检验,x= (-15±√401)/22 ,0 ,-9/5是原方程的解.