Answer
$6x+3h-5$
Work Step by Step
We distribute and simplify the top terms:
$\displaystyle \frac{3(x+h)^{2}-5(x+h)-(3x^{2}-5x)}{h}=\frac{3x^{2}+6xh+3h^{2}-5x-5h-3x^{2}+5x}{h}=\frac{6xh+3h^{2}-5h}{h}$
Then we factor out $h$ and simplify:
$\displaystyle=\frac{h(6x+3h-5)}{h}=6x+3h-5$
