1. **State the problem:** Simplify the expression $\frac{n \times n + n}{n} = 10$ and solve for $n$. 2. **Write the expression clearly:** The numerator is $n \times n + n$, which is $n^2 + n$. The denominator is $n$. So the expression is: $$\frac{n^2 + n}{n} = 10$$ 3. **Simplify the fraction:** Since $n \neq 0$, we can 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. **Check the solution:** Substitute $n=9$ back into the original expression: $$\frac{9 \times 9 + 9}{9} = \frac{81 + 9}{9} = \frac{90}{9} = 10$$ This confirms the solution is correct. **Final answer:** $$n = 9$$