https://file.aiquickdraw.com/mathbot/file/1724573624783hkqzd53u.jpg

The expression given in the image is:

\[
\frac{n^2 + n + 12}{n}
\]

Let's simplify this expression.

### Step-by-step Simplification

1. **Separate Terms**: We can separate the terms in the numerator:

   \[
   \frac{n^2 + n + 12}{n} = \frac{n^2}{n} + \frac{n}{n} + \frac{12}{n}
   \]

2. **Simplify Each Term**:

   \[
   = n + 1 + \frac{12}{n}
   \]

### Final Simplified Expression

The simplified form of the given expression is:

\[
n + 1 + \frac{12}{n}
\]

Would you like more details or have any questions?

### Related Questions

1. What values of \( n \) make \( \frac{12}{n} \) a natural number?
2. How can you check if a number is a divisor of another number?
3. What happens if we change the constant 12 to another number in the expression?
4. How can this type of problem help in learning algebraic manipulation?
5. Can we generalize this approach to more complex polynomials?

### Tip

When simplifying algebraic expressions, look for common factors and ways to decompose the expression to make it easier to handle.

Learn how to simplify the expression (n^2 + n + 12) / n step-by-step. This problem involves algebraic fraction simplification and covers key concepts such as separating terms and simplifying fractions. Suitable for students in Grades 7-9.

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