Answer
$=-\dfrac{1}{(x+3)(x+h+3)}$
Work Step by Step
With $f(x)=\dfrac{1}{x+3}$, the difference quotient is:
$\dfrac{f(x+h)-f(x)}{h}$
$=\dfrac{\dfrac{1}{(x+h) +3}-\dfrac{1}{x+3}}{h}$
$=\dfrac{\dfrac{1}{x+h+3}-\dfrac{1}{x+3}}{h}$
$=\dfrac{\dfrac{(x+3)-(x+h+3)}{(x+h+3)(x+3)}}{h}$
$=\dfrac{\dfrac{x+3-x-h-3}{(x+h+3)(x+3)}}{h}$
$=\dfrac{\dfrac{-h}{(x+h+3)(x+3)}}{h}$
$=-\dfrac{1}{(x+h+3)(x+3)}$
