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a) If there are any cancellations, then the roots of the cancelled terms are candidates for the occurence of holes. The domain of f is all real numbers except -5 and 5. So it's POSSIBLE for the function to have holes there.
b) The function becomes, after cancellation,
. So there is a vertical asymptote at x = -5.
was cancelled from the top and the bottom. Its roots are
-5 and 5. Since there is a vertical asymptote at x = -5, there is a "hole" at the graph only at x = 5. The expression
is never zero for real values of x. (The roots are imaginary.)