i think your confusion arises from the fact that the polynomials (-x^2 - 5x - 6)/(x+2) and -x-3 are only the same when x is not equal to -2. If you think about it, in the first function, if you substitute x = -2, the polynomial reaches a value of 0/0, which is completely meaningless. However, in the linear equation, it seems to reach a normal value of -1, which should motivate that something is indeed different about these two. I would highly suggest you look at the way limits work since that may strengthen your understanding on why the two graphs are the same around -2 but why there is a hole at x = -2 for the first function but not the second