1. **State the problem:** Find the limit $$\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$$. 2. **Recall the formula and rules:** Direct substitution gives $$\frac{3^2 - 9}{3 - 3} = \frac{9 - 9}{0} = \frac{0}{0}$$, which is an indeterminate form. We need to simplify the expression. 3. **Factor the numerator:** $$x^2 - 9 = (x - 3)(x + 3)$$. 4. **Simplify the expression:** $$\frac{(x - 3)(x + 3)}{x - 3} = x + 3$$ for all $$x \neq 3$$. 5. **Evaluate the limit:** Now substitute $$x = 3$$ into the simplified expression: $$3 + 3 = 6$$. 6. **Conclusion:** The limit is $$6$$.