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The expression you are being asked to simplify is:

\[
\frac{x^2y + xy + xy^3}{xy}
\]

### Step-by-step simplification:

1. **Split the terms in the numerator** over the common denominator \( xy \):
   \[
   \frac{x^2y}{xy} + \frac{xy}{xy} + \frac{xy^3}{xy}
   \]

2. **Simplify each term individually**:
   - \(\frac{x^2y}{xy} = \frac{x^2}{x} = x\)
   - \(\frac{xy}{xy} = 1\)
   - \(\frac{xy^3}{xy} = y^2\)

3. **Final simplified expression**:
   \[
   x + 1 + y^2
   \]

Thus, the simplest form of the given expression is \( x + 1 + y^2 \).

The correct answer is the third option: \( x + 1 + y^2 \).

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Would you like further details or have any questions?

Here are five questions that build on this concept:
1. What is the process for simplifying complex algebraic fractions?
2. How can terms be split over a common denominator?
3. How does factor cancellation work in algebraic expressions?
4. Can this method be applied to more complicated algebraic functions?
5. What is the role of exponents when simplifying polynomial terms?

**Tip:** Always check if all terms in the numerator share a common factor with the denominator before simplifying!

Express in simplest terms: (x^2y + xy + xy^3) / xy

Learn how to simplify the algebraic expression (x^2y + xy + xy^3) / xy. This problem covers key algebra concepts such as polynomial division and fraction simplification. Suitable for students in Grades 9-11.

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