If you would like to simplify (15x^2 - 24x + 9) / (3x - 3), you can do this using the following steps:
15x^2 - 24x + 9 = 3 * (5x - 3) * (x - 1)
3x - 3 = 3 * (x - 1)
(15x^2 - 24x + 9) / (3x - 3) = 3 * (5x - 3) * (x - 1) / 3 * (x - 1) = 5x - 3 for x != 1
The correct result would be 5x - 3 for x != 1.