1. **State the problem:** Simplify the expression $\frac{nx n + n}{n}$ and find its value when it equals 10. 2. **Rewrite the expression:** The expression is $\frac{nx n + n}{n}$. Assuming $nx n$ means $n \times n = n^2$, the expression becomes $\frac{n^2 + n}{n}$. 3. **Use the property of fractions:** $\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$, so $$\frac{n^2 + n}{n} = \frac{n^2}{n} + \frac{n}{n}.$$ 4. **Simplify each term:** $$\frac{n^2}{n} = n$$ $$\frac{n}{n} = 1$$ 5. **Combine the simplified terms:** $$n + 1$$ 6. **Set the expression equal to 10:** $$n + 1 = 10$$ 7. **Solve for $n$:** $$n = 10 - 1 = 9$$ **Final answer:** $n = 9$