1. Stating the problem: Solve the equation $$\frac{n \times n + n}{n} = 10$$ for $n$. 2. Write the expression clearly: $$\frac{n^2 + n}{n} = 10$$. 3. Simplify the fraction by dividing each term in the numerator by $n$: $$\frac{n^2}{n} + \frac{n}{n} = 10$$. 4. Simplify each term: $$n + 1 = 10$$. 5. Solve for $n$: Subtract 1 from both sides to get $$n = 10 - 1$$. 6. Calculate the result: $$n = 9$$. Final answer: $n = 9$.