y=(x^2 + 2)/ (3x^2 - 5)
Is the asymptote at
x= sqrt. 5/3
y=o
vertical asymptote is ok
horizontal asymptote is at y=1/3
(x^2+2)/(3x^2-5)
= (1 + 2/x^2) / (3 - 5/x^2)
as x gets huge, the fractions vanish, and we are left with 1/3
When the degree of top and bottom are the same, then the limit is the ratio of the coefficients of the highest power.