Is there a hole ( removable discontinuity ) in this graph. If so where is it, explain reasoning

Question

Is there a hole ( removable discontinuity ) in this graph. If so where is it, explain reasoning.

y= 5x^2+19x-4/ 3x^2+14x+8

Answer 1

In order to answer this question, we need to factor the numerator and denominator. Doing so, we end up with:

y = ((5x - 1)(x + 4)) / ((3x + 2)(x + 4))

Since (x+4) appears in both the numerator and denominator, there is a hole in the graph at x=-4.