Answer
$-\frac{1}{9}$
Work Step by Step
$\lim\limits_{x \to 3}\frac{\frac{1}{x}-\frac{1}{3}}{x-3}=\lim\limits_{x \to 3}\frac{\frac{3}{3x}-\frac{x}{3x}}{x-3}=\lim\limits_{x \to 3}\frac{3-x}{3x(x-3)}=\lim\limits_{x \to 3}\frac{-(x-3)}{3x(x-3)}=\lim\limits_{x \to 3}\frac{-1}{3x}=\frac{-1}{3(3)}=-\frac{1}{9}$
