The expression you provided is:

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

To simplify this, notice that the denominator is a difference of squares:

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

Now, rewrite the original expression using this fact:

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

Since \( x - 2 \) appears in both the numerator and denominator, you can cancel out \( x - 2 \) (as long as \( x \neq 2 \), because division by zero is undefined):

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

Thus, the simplified form of the expression is:

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

### Do you want more details or have any questions?

Here are five related questions:

1. How would you handle this expression if \( x = 2 \)?
2. What is the simplified form of \(\frac{x^2 - 4}{x^2 - 9}\)?
3. How do you simplify \(\frac{x^2 - 4x}{x^2 - 4}\)?
4. Can you find the domain of the function \(\frac{1}{x + 2}\)?
5. How would the simplification change if the denominator was \( x^2 + 4 \) instead of \( x^2 - 4 \)?

### Tip: Always check for factorable patterns like differences of squares when simplifying expressions.

Learn how to simplify the rational expression X-2 over X²-4. This solution involves factoring the difference of squares and canceling common factors. Perfect for students in Grades 8-10 looking to understand key algebraic concepts related to rational expressions.

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