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.