Expand: `(3a+ (2)/(b)) (2a- (3)/(b))`

Answer

To expand the expression \((3a + \frac{2}{b})(2a - \frac{3}{b})\), we will use the distributive property, also known as the FOIL method (First, Outside, Inside, Last) for multiplying two binomials.

### Step-by-Step Solution:

1. **Identify the terms**: We have two binomials: \(3a + \frac{2}{b}\) and \(2a - \frac{3}{b}\).

2. **Apply the distributive property**:
\[ (3a + \frac{2}{b})(2a - \frac{3}{b}) = 3a \cdot 2a + 3a \cdot \left(-\frac{3}{b}\right) + \frac{2}{b} \cdot 2a + \frac{2}{b} \cdot \left(-\frac{3}{b}\right) \]

3. **Calculate each term**:
- First: \(3a \cdot 2a = 6a^2\)
- Outside: \(3a \cdot \left(-\frac{3}{b}\right) = -\frac{9a}{b}\)
- Inside: \(\frac{2}{b} \cdot 2a = \frac{4a}{b}\)
- Last: \(\frac{2}{b} \cdot \left(-\frac{3}{b}\right) = -\frac{6}{b^2}\)

4. **Combine the results**:
\[ 6a^2 - \frac{9a}{b} + \frac{4a}{b} - \frac{6}{b^2} \]

5. **Combine like terms**:
- Combine \(-\frac{9a}{b}\) and \(\frac{4a}{b}\):
\[ -\frac{9a}{b} + \frac{4a}{b} = -\frac{5a}{b} \]

6. **Final expression**:
\[ 6a^2 - \frac{5a}{b} - \frac{6}{b^2} \]

### Final Answer:
\[ 6a^2 - \frac{5a}{b} - \frac{6}{b^2} \]