1. **State the problem:** Simplify the expression $$\frac{2}{x+5} + \frac{2}{x^2+25}$$. 2. **Identify the denominators:** The denominators are $x+5$ and $x^2+25$. 3. **Factor if possible:** Note that $x^2+25$ cannot be factored further over the reals. 4. **Find the common denominator:** The common denominator is $(x+5)(x^2+25)$. 5. **Rewrite each fraction with the common denominator:** $$\frac{2}{x+5} = \frac{2(x^2+25)}{(x+5)(x^2+25)}$$ $$\frac{2}{x^2+25} = \frac{2(x+5)}{(x+5)(x^2+25)}$$ 6. **Add the numerators:** $$2(x^2+25) + 2(x+5) = 2x^2 + 50 + 2x + 10 = 2x^2 + 2x + 60$$ 7. **Write the combined fraction:** $$\frac{2x^2 + 2x + 60}{(x+5)(x^2+25)}$$ 8. **Factor numerator if possible:** $$2x^2 + 2x + 60 = 2(x^2 + x + 30)$$ 9. **Final simplified expression:** $$\frac{2(x^2 + x + 30)}{(x+5)(x^2+25)}$$ This is the simplified form since $x^2 + x + 30$ does not factor nicely over the reals.