If there is a common factor between the numerator and the denominator, and a factor yields a real zero, then the graph will have a hole.

Consider the rational function having common factor.

.

Factorize the numerator and denominator.

Cancel the common terms.

.

Substitute .

.

The function has hole at .

Graph the function: .

.

If there is a common factor between the numerator and the denominator, and a factor yields a real zero, then the graph will have a hole.