\(\frac{15x^{2}-24x+9}{3x-3}\)
Simplify (factor and divide out a 3 from both the top and the bottom)
\(\frac{3(5x^{2}-8x+3)}{3(x-1)}=\frac{5x^{2}-8x+3}{x-1}\)
Factor the top
\(\frac{5x^{2}-8x+3}{x-1}=\frac{5x^{2}-5x-3x+3}{x-1}=\frac{5x^{2}-5x-(3x-3)}{x-1}\)
\(=\frac{5x(x-1)-3(x-1)}{x-1}=\frac{(5x-3)(x-1)}{(x-1)}\)
Divide out a common factor
\(\frac{(5x-3)(x-1)}{(x-1)}=5x-3\)
Therefore your final answer is 5x-3.
Hope this helps!
