解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4

解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4
解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4

解分式方程【x²+1/x+1】+【3(x+1)/x²+1】=4
令t=(x²+1)/(x+1)
则方程化为：t+3/t=4
即t²-4t+3=0
(t-1)(t-3)=0
t=1,3
t=1时,x²+1=x+1,得：x(x-1)=0,得：x=0,1
t=3时,x²+1=3x+3,得：x²-3x-2=0,得:x=(3±√17)/2
经检验,以上4个解都为原方程的解.