1. **State the problem:** Divide the expression $\frac{x^2 + x}{x}$ and set it equal to 10. 2. **Use the division rule:** When dividing polynomials, divide each term in the numerator by the denominator separately. 3. **Divide each term:** $$\frac{x^2}{x} + \frac{x}{x} = x + 1$$ 4. **Set the expression equal to 10:** $$x + 1 = 10$$ 5. **Solve for $x$:** $$x = 10 - 1$$ $$x = 9$$ 6. **Final answer:** $$x = 9$$