 f(x) = (x2 – 4)/(x – 2) = [(x – 2)(x + 2)]/(x – 2) = x + 2

The function you're working with is \( f(x) = \frac{x^2 - 4}{x - 2} \), and you're simplifying it. Let's go through the steps carefully:

1. **Factor the numerator**:  
   The expression \( x^2 - 4 \) is a difference of squares, which can be factored as:
   \[
   x^2 - 4 = (x - 2)(x + 2)
   \]
   So the function becomes:
   \[
   f(x) = \frac{(x - 2)(x + 2)}{x - 2}
   \]

2. **Simplify the expression**:  
   As long as \( x \neq 2 \), we can cancel the \( (x - 2) \) terms from the numerator and denominator:
   \[
   f(x) = x + 2
   \]

   However, you must be careful about domain restrictions. The original expression \( \frac{x^2 - 4}{x - 2} \) is undefined at \( x = 2 \), because the denominator would be zero at this point.

Thus, the simplified function is:
\[
f(x) = x + 2, \quad \text{for} \quad x \neq 2
\]

To summarize:
- The simplified function is \( f(x) = x + 2 \).
- However, \( f(x) \) is **undefined at \( x = 2 \)** due to the original denominator.

Would you like to go deeper into understanding the domain of the function or more details?

### 5 Related Questions:
1. What is the domain and range of the function \( f(x) = \frac{x^2 - 4}{x - 2} \)?
2. How do we determine if a function has a hole in its graph?
3. Can you explain how limits relate to the simplification of this function at \( x = 2 \)?
4. What happens to the graph of \( f(x) = \frac{x^2 - 4}{x - 2} \) near \( x = 2 \)?
5. Why can't we cancel terms if \( x = 2 \)?

### Tip:
Always remember to check for restrictions on the domain when simplifying rational expressions to avoid canceling terms that lead to undefined points.

f(x) = (x^2 – 4)/(x – 2) = [(x – 2)(x + 2)]/(x – 2) = x + 2

Learn how to simplify the rational function f(x) = (x^2 – 4)/(x – 2) by factoring the difference of squares. Understand domain restrictions and why the function is undefined at x = 2. Suitable for high school students, Grades 9-12.

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