graph verticle asymptote of equations

Question

Let f(x)=(x−4)(x+8)(x+7) / (x−4)^2 (x+8)(x+9)

The graph of ff has vertical asymptote(s) of equation(s) ? x =_________ 

(If there are more than one value, seperate them with commas.)

The graph of f has hole(s) at the point(s) of coordinates=____________

Answer 1

Rational functions have a hole when where the common factors of the numerator and the denominator = 0. Therefore to find the holes we first see that the numerator and denominator have common factors of (x-4) and (x+8) but since x-4 doesnt cancel completely we can ignore it for now

solving x+8 = 0 we get a hole at (8,1/12)

Rational functions have asymptotes where the simplified denominator = 0. Therefore when we cancel out the common factors in the numerator and denominator we get that

f(x) = (x+7)/(x-4)(x+9)

solving (x-4)(x+9) = 0

we get asympotes at x=4 and x=-9