1. Problem statement: Solve the equation $$\frac{n^2 + n}{n} = 10$$. 2. Formula and rules: We simplify the rational expression by dividing each term in the numerator by $n$, which is allowed only if $n \neq 0$. 3. Intermediate work: $$\frac{n^2 + n}{n} = \frac{n^2}{n} + \frac{n}{n} = n + 1$$. 4. Solve: Set $n + 1 = 10$ and subtract 1 from both sides to obtain $n = 9$. 5. Check and domain: The original expression requires $n \neq 0$; $n = 9$ satisfies this and when substituted gives $$\frac{9^2 + 9}{9} = \frac{81 + 9}{9} = \frac{90}{9} = 10$$. 6. Final answer: $n = 9$.