1. **State the problem:** Simplify the expression $$\frac{n \times n + n}{n} = 10$$ and solve for $n$. 2. **Rewrite the expression:** The numerator is $n \times n + n$, which is $n^2 + n$. 3. **Apply the division:** $$\frac{n^2 + n}{n} = \frac{n^2}{n} + \frac{n}{n} = n + 1$$ 4. **Set the simplified expression equal to 10:** $$n + 1 = 10$$ 5. **Solve for $n$:** Subtract 1 from both sides: $$n = 10 - 1 = 9$$ 6. **Final answer:** $$n = 9$$