Response to Asymptotes v. Holes

Casey Blue, I believe you answered your own question. It is true that when you have a graph with a numerator and denominator where both the numerator and denominator have the same factor to cancel out. Of course the result in the case we refer to we get a line from the resulting equation, but to prevent the original equation from being undefined, the line has a hole where the zero of the denominator is located.
Secondly, I do hope someone can find an easier way to do 107 in 5.3 because the only way I see is guess and check. Boy is this long.