1. **State the problem:** Find the limit $$\lim_{x \to 3} \frac{x^2 - 9}{x - 3}$$. 2. **Recall the formula and rules:** This is a limit of a rational function where direct substitution leads to a $$\frac{0}{0}$$ indeterminate form. We use algebraic simplification to resolve this. 3. **Factor the numerator:** $$x^2 - 9 = (x - 3)(x + 3)$$. 4. **Rewrite the expression:** $$\frac{x^2 - 9}{x - 3} = \frac{(x - 3)(x + 3)}{x - 3}$$. 5. **Cancel the common factor:** $$\frac{\cancel{(x - 3)}(x + 3)}{\cancel{(x - 3)}} = x + 3$$. 6. **Evaluate the limit by direct substitution:** $$\lim_{x \to 3} (x + 3) = 3 + 3 = 6$$. **Final answer:** $$6$$