\[ \begin{split} &\lim_{x \to 3}\frac{x^2-6x+9}{x^2-9} =\\[15pt] &=\lim_{x \to 3}\frac{(x-3)^2}{(x-3)(x+3)}=\\[15pt] &=\lim_{x \to 3}\frac{x-3}{x+3}=\\[15pt] &=\frac{0}{6}=0 \end{split} \]