Divide the sum of `(-13)/(5) and (4)/(-15) ` by their difference.

Answer

To solve the problem of dividing the sum of \(-\frac{13}{5}\) and \(-\frac{4}{15}\) by their difference, we can break it down into clear steps.

### Step-by-Step Solution:

1. **Identify the sum and difference**:
- We need to find the sum:
\[ \text{Sum} = -\frac{13}{5} + \left(-\frac{4}{15}\right) \]
- And the difference:
\[ \text{Difference} = -\frac{13}{5} - \left(-\frac{4}{15}\right) \]

2. **Calculate the sum**:
- To add these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 15 is 15.
- Convert \(-\frac{13}{5}\) to a fraction with a denominator of 15:
\[ -\frac{13}{5} = -\frac{13 \times 3}{5 \times 3} = -\frac{39}{15} \]
- Now add:
\[ \text{Sum} = -\frac{39}{15} - \frac{4}{15} = -\frac{39 + 4}{15} = -\frac{43}{15} \]

3. **Calculate the difference**:
- For the difference, we convert \(-\frac{4}{15}\) to a fraction with a denominator of 5:
\[ -\frac{4}{15} = -\frac{4 \times 1}{15 \times 1} = -\frac{4}{15} \]
- Now subtract:
\[ \text{Difference} = -\frac{13}{5} + \frac{4}{15} = -\frac{39}{15} + \frac{4}{15} = -\frac{39 - 4}{15} = -\frac{35}{15} \]

4. **Divide the sum by the difference**:
- Now we have:
\[ \text{Sum} = -\frac{43}{15}, \quad \text{Difference} = -\frac{35}{15} \]
- To divide these fractions:
\[ \text{Result} = \frac{-\frac{43}{15}}{-\frac{35}{15}} = \frac{43}{35} \]

### Final Answer:
The final answer is:
\[ \frac{43}{35} \]