Question

x^3+x / x+1
what is the horiztonal asymptote?

Answer 1

I hate to have to harp on this constantly, but you need to indicate, with parentheses whether you mean (x^3 +x)/(x +1) or x^3 + [x/(x+1)].

In one case, the function approaches x^2 for large |x|, and in the other case it approaches x^3. In both cases, there is no horizontal asymptote.