The expression you provided is:

\[
u = \frac{x^2 + \frac{y^2}{xy} + 2y^2}{1}
\]

Let’s break this down step by step to simplify:

### 1. Simplify the denominator of the second term:
The second term is \( \frac{y^2}{xy} \), which simplifies as follows:
\[
\frac{y^2}{xy} = \frac{y}{x}
\]

### 2. Rewrite the expression:
Substituting the simplified form, we get:
\[
u = x^2 + \frac{y}{x} + 2y^2
\]

This is the simplified expression for \( u \).

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Do you have any questions or want further details?

Here are five questions based on this:

1. Can this expression be factored further?
2. What happens to \( u \) when \( y = 0 \)?
3. How does \( u \) behave as \( x \to 0 \)?
4. What is the derivative of \( u \) with respect to \( x \)?
5. Can this expression be used in any specific applications?

**Tip**: Always check for common factors in terms before simplifying further!

This problem involves simplifying the rational expression u = x^2 + y^2 / xy + 2y^2 step-by-step, focusing on algebraic simplification techniques. Learn to break down terms, simplify fractions, and rewrite the expression in a simpler form. Suitable for Grades 9-11.

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