f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6)

Question

Find the equation of the non-vertical asymptote.
What is the smallest value of x at which f(x) intersects its non-vertical asymptote?

Answer 1

since for large x, f(x) just looks like x^3/-3x^2, the asymptote is y = -x/3

So, how to find there the curve intersects the asymptote? Duh. Set the two equal:

(x^3-3x^2-3x-8)/(-3x^2-4x-6) = -x/3

It appears they do not intersect. Typo?