Question

Determine where the rational function is undefined. Determine whether an asymptote or a hole appears at such numbers.

Answer 1

Step 1:

The rational function is .

Cancel the common terms.

The binomial is cancel.

So this is a hole, not an asymptote.

Therefore,  is a hole of .

Step 2:

Find the domain of .

A rational function is undefined at zeros of the denominator.

Find the zeros of denominator.

Domain of rational function is all real numbers except at .

And it is vertical asymptote is .

Solution:

Asymptote is .

Hole is .