1. **State the problem:** Simplify the expression $$\frac{x^2 - 4}{x - 2}$$. 2. **Recall the formula and rules:** The numerator is a difference of squares, which factors as $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Factor the numerator:** $$x^2 - 4 = (x - 2)(x + 2)$$ 4. **Rewrite the expression:** $$\frac{(x - 2)(x + 2)}{x - 2}$$ 5. **Cancel the common factor:** $$\frac{\cancel{(x - 2)}(x + 2)}{\cancel{(x - 2)}} = x + 2$$ 6. **State the simplified form:** The simplified expression is $$x + 2$$, with the restriction that $$x \neq 2$$ because the original denominator cannot be zero. **Final answer:** $$x + 2$$ (for $$x \neq 2$$).