1. **State the problem:** We want to simplify and solve the expression $$\frac{n \times n + n}{n} = 10$$ for $n$. 2. **Rewrite the numerator:** The numerator is $$n \times n + n = n^2 + n$$. 3. **Divide each term in the numerator by $n$ separately:** $$\frac{n^2}{n} + \frac{n}{n} = n + 1$$ This works because division distributes over addition. 4. **Set the simplified expression equal to 10:** $$n + 1 = 10$$ 5. **Solve for $n$:** Subtract 1 from both sides: $$n = 10 - 1 = 9$$ **Final answer:** $$n = 9$$