Answer
$2x+h-1.$
Work Step by Step
RECALL: $\\\\$The difference quotient of a function $f$ is given by the formula $\dfrac{f(x+h)-f(x)}{h}$ where $h \ne0$. Use the difference quotient formula above to obtain:
$\dfrac{f(x+h)-f(x)}{h}\\=\dfrac{(x+h)^2-(x+h)+4-(x^2-x+4)}{h}\\=\dfrac{x^2+2xh+h^2-x-h+4-x^2+x-4}{h}\\=\dfrac{2xh+h^2-h}{h}\\=2x+h-1.$
