1. **State the problem:** Find the limit $ \lim_{x \to 3} \frac{x^2 - 9}{x - 3} $. 2. **Recall the formula and rules:** The limit of a rational function as $ x $ approaches a value can often be found by simplifying the expression, especially if direct substitution leads to an indeterminate form like $ \frac{0}{0} $. 3. **Evaluate the expression directly:** Substitute $ x = 3 $ into the numerator and denominator: $$\frac{3^2 - 9}{3 - 3} = \frac{9 - 9}{0} = \frac{0}{0}$$ This is an indeterminate form, so we need to simplify. 4. **Factor the numerator:** $$x^2 - 9 = (x - 3)(x + 3)$$ 5. **Rewrite the expression:** $$\frac{(x - 3)(x + 3)}{x - 3}$$ 6. **Cancel the common factor $ x - 3 $:** $$\frac{\cancel{(x - 3)}(x + 3)}{\cancel{x - 3}} = x + 3$$ 7. **Evaluate the simplified expression at $ x = 3 $:** $$3 + 3 = 6$$ **Final answer:** $$\lim_{x \to 3} \frac{x^2 - 9}{x - 3} = 6$$