Question

Describe the vertical asymptote(s) and hole(s) for the graph of (x-5)(x-2)/(x-2)(x+4)

Answer 1

The equation simplifies into being (x-5)/(x+4), since the (x-2) terms cancel out, right?

So, there's a vertical asymptote at x=-4, since that would make the expression have a 0 in the denominator, not allowed.

However, from the original expression, we also cannot have x=2, since that would put a zero in the original denominator, which means we'll have a hole at x=2.