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Let's simplify the given expression:

\[
\frac{6x^2 y}{z} + \frac{3xy^2}{z}
\]

Since both terms have the same denominator \( z \), we can combine them as follows:

\[
\frac{6x^2 y + 3xy^2}{z}
\]

Now, let's factor the numerator:

\[
6x^2 y + 3xy^2 = 3xy(2x + y)
\]

So the expression becomes:

\[
\frac{3xy(2x + y)}{z}
\]

This is the simplified form. Now, let's match it with the given options:

- A) \(\frac{2x^2}{y^2}\)
- B) \(\frac{3x}{y}\)
- C) \(\frac{2x}{y}\)
- D) \(\frac{6y}{xz}\)

None of these exactly match the simplified form, but the simplified version \(\frac{3xy(2x + y)}{z}\) does not directly correspond to any of the choices provided, which suggests there might be a need to recheck the options or their formulation.

Do you want further details on any specific part of this solution? 
Here are five related questions for further practice:
1. How do you simplify expressions with a common denominator?
2. How do you factor common terms in a polynomial?
3. What is the process for simplifying rational expressions?
4. How can you combine like terms when they involve variables?
5. How do you check if two algebraic expressions are equivalent?

**Tip:** Always look for common factors in the numerator to simplify complex algebraic expressions.

Simplify the expression 6x^2y/z + 3xy^2/z

Learn how to simplify the algebraic expression 6x^2y/z + 3xy^2/z. This problem covers key algebraic concepts, such as rational expressions, combining like terms, and factoring. Suitable for students in Grades 9-10.

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