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.