Question

Determine the holes, vertical asymptotes, and horizontal asymptotes of the rational function y=3x^2+10x-8/x^2+7x+12

I have the vertical and horizontal asymptotes which are x=-3 and y=3, but I'm having trouble finding the holes. Could someone help me out with that?

Answer 1

There would be a hole when x = -4.

If you factor both the top and the bottom, you will see that the factor (x + 4) is in both the numerator and denominator. Therefore, the would be a hole when x = -4 because that would also make the denominator 0.