1. **State the problem:** Find the limit $ \lim_{x \to 3} \frac{x^2 - 9}{x - 3} $. 2. **Recall the formula and rules:** The expression is a rational function. Direct substitution $ x=3 $ gives $ \frac{3^2 - 9}{3 - 3} = \frac{0}{0} $, an indeterminate form. We need to simplify the expression. 3. **Factor the numerator:** $ x^2 - 9 = (x - 3)(x + 3) $. 4. **Rewrite the limit:** $$ \lim_{x \to 3} \frac{(x - 3)(x + 3)}{x - 3} $$ 5. **Cancel the common factor:** $$ \lim_{x \to 3} \frac{\cancel{(x - 3)}(x + 3)}{\cancel{(x - 3)}} = \lim_{x \to 3} (x + 3) $$ 6. **Evaluate the simplified limit:** $$ \lim_{x \to 3} (x + 3) = 3 + 3 = 6 $$ **Final answer:** $6$