lim x:3 1/x - 1/3 /x - 3

As follows

$\lim_{x\rightarrow 3}\frac{1/x-1/3}{x-3}\rightarrow \lim_{x\rightarrow 3}\frac{3-x}{3x(x-3)} \rightarrow \lim_{x\rightarrow 3}\frac{-1}{3x} \rightarrow \frac{-1}{9}$