1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n} = 10$$ and solve for $n$. 2. **Write the expression clearly:** $$\frac{n^2 + n}{n} = 10$$ 3. **Simplify the fraction:** Since $n \neq 0$, divide each term in the numerator by $n$: $$\frac{n^2}{n} + \frac{n}{n} = n + 1$$ 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 $9$.