A rational function will have a hole if there is a factor that is the same in both the numerator and the denominator. This is because the factor can be cancelled out, leaving an undefined point in the function, which is the hole. For example, consider the rational function f(x) = (x - 2)(x + 3) / (x - 2)(x - 1). In this function, the factor (x - 2) is present in both the numerator and the denominator. Therefore, it can be cancelled out, simplifying the function to f(x) = (x + 3) / (x - 1). However, the original function was undefined at x = 2, because if you substitute x = 2 into the denominator of the original function, you get 0, which makes the function undefined. So, even though the simplified function is defined at x = 2, the original function was not. Therefore, there is a hole at x = 2. To find the y-coordinate of the hole, you substitute x = 2 into the simplified function, giving you (2 + 3) / (2 - 1) = 5. So, the hole in the function is located at the point (2, 5)