If a rational function is defined as $f(x) = \frac{p(x)} {q(x)}$ for any two polynomials $p(x)$ and $q(x)$; given $p(x) = 2x+1$ (polynomial of degree 1) and $q(x) = 3$ (polynomial of degree zero), and the fact that a line $mx+n$ is asymptotic to rational function $f(x)$ if $\lim_{x\to \pm\infty} [f(x) - (mx + n)] = 0$ then by that definition the oblique asymptote of $\frac{2x+1} {3}$ is $\frac 2 3 x + \frac 1 3$
This can't be right though... can it?
Not only is it the asymptote, the function is of course a straight line, so that $f(x)-mx-n$ is always zero.
It's just not horizontal.