1. **State the problem:** Simplify the expression $$\frac{x^2 + x}{x + 10} + \frac{10x + 10}{x + 10}$$. 2. **Identify the common denominator:** Both fractions have the same denominator $x + 10$. 3. **Combine the numerators over the common denominator:** $$\frac{x^2 + x + 10x + 10}{x + 10}$$ 4. **Simplify the numerator:** $$x^2 + x + 10x + 10 = x^2 + 11x + 10$$ 5. **Factor the numerator:** $$x^2 + 11x + 10 = (x + 1)(x + 10)$$ 6. **Rewrite the expression:** $$\frac{(x + 1)(x + 10)}{x + 10}$$ 7. **Cancel the common factor $(x + 10)$ (assuming $x \neq -10$ to avoid division by zero):** $$x + 1$$ **Final answer:** $$x + 1$$