Let's simplify the expression step by step:

The expression is:  
\[
\frac{\frac{y}{3} + \frac{y}{2}}{y} + \frac{y}{2}
\]

### Step 1: Simplify the numerator of the first fraction
The numerator is \(\frac{y}{3} + \frac{y}{2}\).

To add these, we need a common denominator. The least common denominator (LCD) of 3 and 2 is 6. So:

\[
\frac{y}{3} = \frac{2y}{6}, \quad \frac{y}{2} = \frac{3y}{6}
\]

Now, add the two fractions:
\[
\frac{2y}{6} + \frac{3y}{6} = \frac{5y}{6}
\]

### Step 2: Simplify the first part of the expression
The first part becomes:
\[
\frac{\frac{5y}{6}}{y}
\]

This simplifies to:
\[
\frac{5y}{6y} = \frac{5}{6}
\]

### Step 3: Combine the terms
Now we have:
\[
\frac{5}{6} + \frac{y}{2}
\]

### Step 4: Simplify the final expression
We need a common denominator to add \(\frac{5}{6}\) and \(\frac{y}{2}\). The LCD of 6 and 2 is 6, so:

\[
\frac{y}{2} = \frac{3y}{6}
\]

Now, add the two terms:
\[
\frac{5}{6} + \frac{3y}{6} = \frac{5 + 3y}{6}
\]

### Final Simplified Expression:
\[
\frac{5 + 3y}{6}
\]

Let me know if you'd like further details or if you have any questions!

### Related questions:
1. How do you find the least common denominator when adding fractions?
2. How can you simplify complex fractions more efficiently?
3. What are the rules for adding algebraic fractions with different denominators?
4. How can you apply these steps to solve rational expressions in equations?
5. How do common denominators help in simplifying polynomial expressions?

**Tip:** Always look for common denominators when adding or subtracting fractions to simplify the process.

Learn how to simplify the rational expression (y/3 + y/2)/y + y/2 with a step-by-step solution. This problem covers key algebraic concepts, such as the addition of fractions with different denominators and simplification of complex fractions. Suitable for students in Grades 8-10.

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