Question

Use the function, x^2-2x-35/x^2-x-30 to find and any discontinuities.

Answer 1

Discontinuities occur when there is a hole (a factor of zero over the same factor) or a zero factor in the denominator. So factor top and bottom giving:
\[\frac{(x-7)(x+5)}{(x-6)(x+5)}\]
So you have a hole at x=-5 and a vertical asymptote at x=6.