The given limit is:

\[
\lim_{x \to 3} \frac{x^2 - 9}{x - 3}
\]

### Step 1: Factor the numerator
The numerator \(x^2 - 9\) can be factored as a difference of squares:

\[
x^2 - 9 = (x - 3)(x + 3)
\]

### Step 2: Simplify the expression
Substitute the factored form into the expression:

\[
\frac{(x - 3)(x + 3)}{x - 3}
\]

For \(x \neq 3\), the terms \(x - 3\) cancel out, leaving:

\[
x + 3
\]

### Step 3: Evaluate the limit
Now, substitute \(x = 3\) into the simplified expression:

\[
x + 3 = 3 + 3 = 6
\]

Thus, the limit is:

\[
\boxed{6}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What is the definition of a limit in calculus?
2. How do we deal with indeterminate forms like \( \frac{0}{0} \)?
3. How can limits be used to define the derivative of a function?
4. What are some common techniques for evaluating limits?
5. What is the difference between one-sided and two-sided limits?

**Tip:** Always check if factoring or other algebraic manipulations can simplify a limit expression before applying direct substitution.

Learn how to evaluate the limit lim x -> 3 (x^2 - 9)/(x - 3) using algebraic manipulation and substitution. This problem involves limits and algebra, focusing on the difference of squares formula. Suitable for Grades 11-12.

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