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 that becomes indeterminate of the form $$\frac{0}{0}$$ when substituting $x=3$. To resolve this, factor the numerator and simplify. 3. **Factor the numerator:** $$x^2 - 9 = (x - 3)(x + 3)$$. 4. **Simplify the expression:** $$\frac{x^2 - 9}{x - 3} = \frac{(x - 3)(x + 3)}{x - 3}$$. 5. **Cancel common factors:** For $x \neq 3$, $$\frac{(x - 3)(x + 3)}{x - 3} = x + 3$$. 6. **Evaluate the limit:** Substitute $x = 3$ into the simplified expression: $$3 + 3 = 6$$. **Final answer:** $$\lim_{x \to 3} \frac{x^2 - 9}{x - 3} = 6$$.