\(\frac{15x^{2} - 24x + 9}{3x - 3} = \frac{3(5x^{2}) - 3(8x) + 3(3)}{3(x) - 3(1)} = \frac{3(5x^{2} - 8x + 3)}{3(x - 1)} = \frac{5x^{2} - 8x + 3}{x - 1} = \frac{5x^{2} - 5x - 3x + 3}{x - 1} = \frac{5x(x) - 5x(1) - 3(x) - 3(-1)}{x - 1} = \frac{5x(x - 1) - 3(x - 1)}{x - 1} = \frac{(5x - 3)(x - 1)}{x - 1} = 5x - 3\)
The answer is C.
