曲线y=3x^2+1/(x-1)(x-2)的渐近线有

y=(3x^2+1)/[(x-1)(x-2)]
x-->1时,y-->∞,
x-->2时,y-->∞
∴x=1和x=2为垂直渐近线
又lim( x-->∞ )(3x^2+1)/[(x-1)(x-2)]
=lim( x-->∞ )(3+1/x²)/[(1-1/x)(1-2/x)]
=(3+0)/[(1-0)(1-0)]
=3
∴x=3是水平渐近线
∴曲线的渐近线有x=1,x=2,y=3