Answer
$2a+h+3$.
Work Step by Step
Plug $x=(a+h)$ into the function $f(x)$ to find $f(a+h)$.
$f(a+h)=(a+h)^2+3(a+h)-15$
Simplify.
$f(a+h)=a^2+2ah+h^2+3a+3h-15$
Plug $x=a$ into the function $f(x)$ to find $f(a)$.
$f(a)=a^2+3a-15$.
Substitute the expressions of $f(a+h)$ and $f(a)$ in the required expression.
$\frac{f(a+h)-f(a)}{h}$
$=\frac{a^2+2ah+h^2+3a+3h-15-(a^2+3a-15)}{h}$
Simplify.
$=\frac{a^2+2ah+h^2+3a+3h-15-a^2-3a+15}{h}$
$=\frac{2ah+h^2+3h}{h}$
$=\frac{h(2a+h+3)}{h}$
$=2a+h+3$.
