To find the domain of the function \( f(x) = \frac{x+2}{x-2} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is equal to zero because division by zero is not allowed.

### Steps to find the domain:

1. **Identify the denominator:** The denominator of the function is \( x - 2 \).

2. **Set the denominator equal to zero and solve for \( x \):**
   \[
   x - 2 = 0
   \]
   \[
   x = 2
   \]
   So, the function is undefined when \( x = 2 \).

3. **State the domain:** The domain of the function \( f(x) = \frac{x+2}{x-2} \) includes all real numbers except \( x = 2 \).

### Conclusion:
The domain of \( f(x) = \frac{x+2}{x-2} \) is:
\[
\boxed{x \in \mathbb{R}, x \neq 2}
\]

Would you like further details or have any questions?

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**Related Questions:**

1. What is the range of \( f(x) = \frac{x+2}{x-2} \)?
2. How do you find the vertical asymptotes of a rational function?
3. Can you find the horizontal asymptote of \( f(x) = \frac{x+2}{x-2} \)?
4. How do you graph \( f(x) = \frac{x+2}{x-2} \)?
5. What happens to \( f(x) \) as \( x \) approaches 2 from the left and right?

**Tip:** When finding the domain of a function, always look for values that make the denominator zero, as these points will be excluded from the domain.

Learn how to find the domain of the function f(x) = (x + 2) / (x - 2). Understand why the function is undefined for certain values of x and how to determine the domain. Suitable for students in Grades 10-12 studying rational functions and domain analysis.

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