1. **State the problem:** Simplify the expression $$\frac{3}{a^2-16} + \frac{2}{a+4}$$. 2. **Recall the formula and rules:** The denominator $a^2-16$ is a difference of squares, which factors as $$a^2-16 = (a-4)(a+4)$$. 3. **Rewrite the expression with factored denominators:** $$\frac{3}{(a-4)(a+4)} + \frac{2}{a+4}$$ 4. **Find a common denominator:** The common denominator is $(a-4)(a+4)$. 5. **Rewrite each fraction with the common denominator:** $$\frac{3}{(a-4)(a+4)} + \frac{2}{a+4} = \frac{3}{(a-4)(a+4)} + \frac{2\cancel{(a-4)}}{\cancel{(a+4)}(a-4)}$$ 6. **Combine the fractions:** $$= \frac{3 + 2(a-4)}{(a-4)(a+4)}$$ 7. **Simplify the numerator:** $$3 + 2(a-4) = 3 + 2a - 8 = 2a - 5$$ 8. **Final simplified expression:** $$\frac{2a - 5}{(a-4)(a+4)}$$ This is the simplified form of the original expression.