The expression you provided is:

\[
\frac{x - 2}{x^2 - 4}
\]

To simplify this expression, let's factor the denominator.

### Step 1: Factor the Denominator
Notice that the denominator \(x^2 - 4\) is a difference of squares, which can be factored as follows:

\[
x^2 - 4 = (x - 2)(x + 2)
\]

### Step 2: Simplify the Expression
Now substitute the factored form of the denominator back into the expression:

\[
\frac{x - 2}{(x - 2)(x + 2)}
\]

### Step 3: Cancel Common Factors
Since \(x - 2\) is a common factor in both the numerator and denominator, we can cancel it out (assuming \(x \neq 2\) to avoid division by zero):

\[
\frac{1}{x + 2}
\]

### Final Answer:
The simplified form of the expression is:

\[
\frac{1}{x + 2} \quad \text{(for \(x \neq 2\))}
\]

Would you like any further details or have any questions about this?  

Here are 5 related questions you might find interesting:

1. What happens if \(x = 2\) in the original expression?
2. How would you factor the expression \(x^2 - 9\)?
3. Can you simplify \(\frac{x^2 - 4}{x^2 - 4}\)?
4. How do you find the domain of \(\frac{1}{x + 2}\)?
5. What is the derivative of \(\frac{1}{x + 2}\) with respect to \(x\)?

**Tip:** Always check for restrictions on the variable when simplifying expressions, especially when canceling out terms.

Learn how to simplify the rational expression (x - 2) / (x^2 - 4) step-by-step with detailed explanations. This problem covers key algebraic concepts including factoring, domain considerations, and rational expression simplification. Suitable for high school students (Grades 10-12).

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