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