To simplify the expression \(\frac{5}{\frac{3}{2} - \frac{2}{3}}\), we first need to simplify the denominator.

### Step 1: Simplify the Denominator

The denominator is \(\frac{3}{2} - \frac{2}{3}\). To subtract these fractions, we need a common denominator:

\[
\text{Common denominator of } 2 \text{ and } 3 = 6
\]

Now, convert each fraction:

\[
\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}, \quad \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]

So, the subtraction becomes:

\[
\frac{9}{6} - \frac{4}{6} = \frac{5}{6}
\]

### Step 2: Rewrite the Original Expression

Now the expression is:

\[
\frac{5}{\frac{5}{6}}
\]

### Step 3: Simplify the Expression

To simplify \(\frac{5}{\frac{5}{6}}\), we multiply by the reciprocal of \(\frac{5}{6}\):

\[
5 \times \frac{6}{5} = \frac{5 \times 6}{5} = 6
\]

### Conclusion

The simplified form of the expression is:

\[
\boxed{6}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions

1. How do you find a common denominator when subtracting fractions?
2. How do you simplify a complex fraction?
3. What is the reciprocal of a fraction, and how is it used in division?
4. How can you simplify expressions with nested fractions?
5. How can you verify the correctness of fraction simplifications?

### Tip

When dealing with complex fractions, it helps to simplify each part step-by-step, focusing on one operation at a time.

Learn how to simplify the complex fraction \frac{5}{\frac{3}{2} - \frac{2}{3}} with a detailed, step-by-step solution. This problem focuses on subtracting fractions using a common denominator and simplifying using reciprocals. Perfect for students in Grades 6-8.

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