Question: Find the limit of the expression \( \frac{x^2 - 9}{x - 3} \) as \( x \) approaches 3.
1. **State the problem:**
Find \( \lim_{x \to 3} \frac{x^2 - 9}{x - 3} \).
2. **Recall the formula and rules:**
This is a limit of a rational function where direct substitution leads to \( \frac{0}{0} \), an indeterminate form.
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 substitution:**
\[ \lim_{x \to 3} (x + 3) = 3 + 3 = 6 \]
**Final answer:**
\[ \boxed{6} \]