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Horizontal asymptotes on rational functions

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I haven't heard of that rule before, can you provide an example where it does work?
by
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> 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)

You need an additional rule:

> if the degree of denominator is **larger** to degree of the numerator, then the HA is **zero**

So the HA of 1/x is y=0. Since it's not 1/x but 1/x+2, the HA is not y=0 but y=0+2
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(1/x)+2=(1+2x)/x=(2x+1)/x

Now you can apply the HA rule.

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