1. **State the problem:** Solve the equation $$\frac{n \times n + n}{n} = 10$$ for $n$. 2. **Rewrite the equation:** The numerator is $n \times n + n = n^2 + n$, so the equation becomes $$\frac{n^2 + n}{n} = 10$$. 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 $n$:** Subtract 1 from both sides: $$n = 10 - 1 = 9$$. 6. **Check the solution:** Substitute $n=9$ back into the original equation: $$\frac{9 \times 9 + 9}{9} = \frac{81 + 9}{9} = \frac{90}{9} = 10$$, which is true. **Final answer:** $$n = 9$$.