In this lesson, we learn how to determine the locations of holes in the graph of a rational function which has common factors in both the numerator and denominator. If both the numerator and the denominator have the same factor, x minus b, then there is a hole in the graph at the point where x equals b, unless the line x equals b is a vertical asymptote. We see this process in action by taking an example of f of x equals x squared plus x minus 6 over x minus 2, factoring it out, canceling common factors, and plotting the hole on the graph.
Given a rational function which has common factors in both the numerator and denominator, determine the locations in the graph of the simplified expression where holes would be located.