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.