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The expression you need to evaluate is given as:

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

We are asked to evaluate this when \( x = 6 \) and \( y = 3 \). Let's solve this step-by-step:

### Step 1: Substitute \( x = 6 \) and \( y = 3 \) into the expression
\[
\frac{2(3) + (6)^2}{6}
\]

### Step 2: Simplify the terms inside the numerator
\[
\frac{2(3) + 36}{6} = \frac{6 + 36}{6} = \frac{42}{6}
\]

### Step 3: Perform the division
\[
\frac{42}{6} = 7
\]

Thus, the simplified result of the expression is \( 7 \).

Would you like more details or further clarification?

### Related questions:
1. What happens if we change \(x\) and \(y\) to different values?
2. How would the result change if the expression were \(\frac{2y + x^3}{x}\)?
3. What are some general rules for simplifying expressions like this?
4. How can we use algebra to factor expressions in the numerator?
5. How do you handle similar expressions involving variables in both the numerator and denominator?

**Tip:** Always simplify expressions by performing operations inside parentheses and exponents first, then work outward!

Evaluate the expression when x = 6 and y = 3: (2y + x^2) / x. Simplify your answer as much as possible.

Learn how to evaluate and simplify the algebraic expression (2y + x^2) / x by substituting x = 6 and y = 3. This problem covers key concepts such as substitution, simplifying algebraic expressions, and basic arithmetic. Suitable for students in Grades 6-8.

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