Answer
$ -\frac{3}{a(a+h)}$.
Work Step by Step
The given function is
$\Rightarrow f(x)=\frac{3}{x}$
Replace $x$ with $a+h$.
$\Rightarrow f(a+h)=\frac{3}{a+h}$
Replace $x$ with $a$.
$\Rightarrow f(a)=\frac{3}{a}$
Substitute all the values into
$\Rightarrow \frac{f(a+h)-f(a)}{h}$
$\Rightarrow \frac{\frac{3}{a+h}-\frac{3}{a}}{h}$
Solve the numerator.
$=\frac{3}{a+h}-\frac{3}{a}$
The LCD of the denominators is $a(a+h)$.
$=\frac{3a}{a(a+h)}-\frac{3(a+h)}{a(a+h)}$
$=\frac{3a-3(a+h)}{a(a+h)}$
$=\frac{3a-3a-3h}{a(a+h)}$
Simplify.
$=\frac{-3h}{a(a+h)}$
Back substitute all values into the original fraction.
$\Rightarrow \frac{-3h}{a(a+h)h}$
Simplify.
$\Rightarrow -\frac{3}{a(a+h)}$.
