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To solve the problem of dividing these fractions, you need to follow these steps:

### Problem
\[
\frac{3x}{8} \div \frac{5}{2x}
\]

### Steps to Solve:

1. **Rewrite the Division as Multiplication**: When dividing fractions, you multiply by the reciprocal of the second fraction.
\[
\frac{3x}{8} \times \frac{2x}{5}
\]

2. **Multiply the Numerators**:
\[
3x \times 2x = 6x^2
\]

3. **Multiply the Denominators**:
\[
8 \times 5 = 40
\]

4. **Simplify the Fraction**:
\[
\frac{6x^2}{40}
\]

   - The greatest common factor (GCF) of 6 and 40 is 2.
   - Simplify by dividing both the numerator and the denominator by 2:
\[
\frac{6x^2}{40} = \frac{3x^2}{20}
\]

### Final Answer:
\[
\boxed{\frac{3x^2}{20}}
\]

Would you like any further details or explanations? Here are five related questions you might find interesting:

1. How do you multiply and divide algebraic fractions?
2. What is the process for finding the reciprocal of a fraction?
3. How do you determine the greatest common factor (GCF) when simplifying fractions?
4. Can you divide fractions that contain variables in the denominator?
5. What are some common mistakes to avoid when dividing algebraic fractions?

**Tip:** Always check if the fractions can be simplified before and after performing operations to ensure the simplest form of the answer.

Divide these fractions. Give your answer in its simplest form: (3x/8) ÷ (5/2x).

Learn how to divide algebraic fractions and simplify the result. This example problem covers the division and simplification of the fractions (3x/8) ÷ (5/2x), a key concept in middle school algebra. Suitable for students in Grades 7-9.

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