1. **State the problem:** Simplify the expression $$\frac{2}{x+5} + \frac{2}{x^2-25}$$. 2. **Recognize the formula and rules:** The expression involves adding two rational expressions. To add them, find a common denominator. 3. **Factor the denominator:** Note that $$x^2 - 25$$ is a difference of squares: $$x^2 - 25 = (x+5)(x-5)$$. 4. **Rewrite the expression:** $$\frac{2}{x+5} + \frac{2}{(x+5)(x-5)}$$. 5. **Find common denominator:** The common denominator is $$ (x+5)(x-5) $$. 6. **Rewrite the first fraction with the common denominator:** $$\frac{2}{x+5} = \frac{2(x-5)}{(x+5)(x-5)} = \frac{2x - 10}{(x+5)(x-5)}$$. 7. **Add the fractions:** $$\frac{2x - 10}{(x+5)(x-5)} + \frac{2}{(x+5)(x-5)} = \frac{2x - 10 + 2}{(x+5)(x-5)} = \frac{2x - 8}{(x+5)(x-5)}$$. 8. **Factor numerator if possible:** $$2x - 8 = 2(x - 4)$$. 9. **Final simplified expression:** $$\frac{2(x - 4)}{(x+5)(x-5)}$$. This is the simplified form of the original expression.