令a=(x²+1)/x
则x/(x²+1)=1/a
所以a+2/a=3
a²+2=3a
a²-3a+2=0
(a-1)(a-2)=0
a=1,a=2
(x²+1)/x=a=1
x²+1=x
x²-x+1=0
判别式=(-1)²-4<0,无解
(x²+1)/x=a=2
x²+1=2x
x²-2x+1=0
(x-1)²=0
x=1
所以x=1