Answer
$\dfrac{-1}{9}$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
In order to to find the limit, we will plug $ a $ into the function and then simplify.
$\lim_\limits{x\to 0} \dfrac{\dfrac{1}{x+3}-\dfrac{1}{3}}{x}=\lim_\limits{x\to 0} \dfrac{\dfrac{-x}{3(x+3)}}{x}$
or, $= \lim_\limits{x\to 0} \dfrac{-1}{3(x+3)}$
or, $= \dfrac{-1}{9}$
