Answer
$\displaystyle 2x+h-1$
Work Step by Step
We are given:
$f(x)=x^{2}-x+4$
We find the difference quotient:
$\displaystyle \frac{f(x+h)-f(x)}{h}$
$\displaystyle =\frac{(x+h)^{2}-(x+h)+4-(x^{2}-x+4)}{h}$
$\displaystyle =\frac{x^{2}+2xh+h^{2}-x-h+4-x^{2}+x-4}{h}$
$\displaystyle =\frac{2xh+h^{2}-h}{h}$
$\displaystyle =\frac{h(2x+h-1)}{h}$
$\displaystyle =2x+h-1$