To find the domain of the function \( f(x) = \frac{x + 2}{x^2 - 4} \), we need to determine where the function is defined. This means identifying values of \( x \) for which the denominator is not zero, since division by zero is undefined.

### Step 1: Identify the Denominator
The denominator of the function is:
\[
x^2 - 4
\]
This can be factored as:
\[
x^2 - 4 = (x - 2)(x + 2)
\]

### Step 2: Set the Denominator Equal to Zero
We set the denominator equal to zero to find the values of \( x \) that make the denominator zero:
\[
(x - 2)(x + 2) = 0
\]

### Step 3: Solve for \( x \)
Solving the equation gives:
\[
x - 2 = 0 \quad \text{or} \quad x + 2 = 0
\]
\[
x = 2 \quad \text{or} \quad x = -2
\]

### Step 4: Determine the Domain
The function is undefined at \( x = 2 \) and \( x = -2 \) because these values make the denominator zero. Therefore, the domain of \( f(x) \) is all real numbers except \( x = 2 \) and \( x = -2 \).

### Final Answer
The domain of the function is:
\[
\boxed{(-\infty, -2) \cup (-2, 2) \cup (2, +\infty)}
\]

Would you like more details or have any questions? 

Here are five related questions:
1. How do you determine the zeros of a rational function?
2. What happens to the graph of a function at points where the denominator is zero?
3. How do you find the range of a rational function?
4. What are the steps to factor a quadratic expression like \(x^2 - 4\)?
5. How does factoring help in finding the domain of a rational function?

**Tip:** Always factor the denominator of a rational function to easily identify values that should be excluded from the domain.

Learn how to find the domain of the function f(x) = (x + 2) / (x^2 - 4) step-by-step. Understand where the function is undefined due to division by zero. Suitable for high school students studying rational functions and quadratic equations.

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