1. **State the problem:** Simplify the expression $\frac{x+2}{x^2-4}$. 2. **Recall the formula and rules:** The denominator is a difference of squares, which factors as $a^2 - b^2 = (a-b)(a+b)$. 3. **Factor the denominator:** $$x^2 - 4 = (x - 2)(x + 2)$$ 4. **Rewrite the expression:** $$\frac{x+2}{(x-2)(x+2)}$$ 5. **Cancel common factors:** The numerator and denominator both have a factor of $x+2$. $$\frac{\cancel{x+2}}{(x-2)\cancel{(x+2)}} = \frac{1}{x-2}$$ 6. **State the simplified expression:** $$\frac{1}{x-2}$$ 7. **Important note:** The original expression is undefined at $x=2$ and $x=-2$ because the denominator is zero there. **Final answer:** $$\frac{1}{x-2}$$