1. **State the problem:** Find the limit as $x$ approaches 3 of the function $$\frac{x^2 - 9}{x - 3}$$. 2. **Recall the formula and rules:** The limit of a rational function where direct substitution leads to a $\frac{0}{0}$ indeterminate form can often be found by factoring and simplifying. 3. **Factor the numerator:** $$x^2 - 9 = (x - 3)(x + 3)$$. 4. **Rewrite the expression:** $$\frac{(x - 3)(x + 3)}{x - 3}$$. 5. **Simplify by canceling common factors:** $$\frac{\cancel{(x - 3)}(x + 3)}{\cancel{(x - 3)}} = x + 3$$. 6. **Evaluate the limit by direct substitution:** $$\lim_{x \to 3} (x + 3) = 3 + 3 = 6$$. 7. **Final answer:** The limit is **6**.