1. **State the problem:** Simplify the expression $\frac{n^2 + n}{n}$ and solve for $n$ when the expression equals 10. 2. **Formula and rules:** When dividing a polynomial by a variable, divide each term separately by that variable, assuming $n \neq 0$ to avoid division by zero. 3. **Simplify the expression:** $$\frac{n^2 + n}{n} = \frac{n^2}{n} + \frac{n}{n} = n + 1$$ 4. **Set the simplified expression equal to 10:** $$n + 1 = 10$$ 5. **Solve for $n$:** $$n = 10 - 1 = 9$$ 6. **Conclusion:** The value of $n$ that satisfies the equation is $9$.