Horizontal asymptotes on rational functions

I haven't heard of that rule before, can you provide an example where it does work?
by
> if the **degree** of denominator is **equal** to degree of the numerator
>
>For instance, (1 / x) + 2

The degree of (1) is 0 and the degree of (x) is 1. Even if you ignore the 2 (which you can't), that rule wouldn't apply here (unless you transform it)