To divide \(-\frac{5}{2}\) by \(-\frac{15}{17}\), you can multiply by the reciprocal of the divisor:
\[ -\frac{5}{2} \div -\frac{15}{17} = -\frac{5}{2} \times -\frac{17}{15} \]
The negatives cancel out:
\[ \frac{5}{2} \times \frac{17}{15} \]
Now, multiply the numerators and the denominators:
\[ \frac{5 \times 17}{2 \times 15} = \frac{85}{30} \]
Next, we simplify \(\frac{85}{30}\). The greatest common divisor (GCD) of 85 and 30 is 5. So, we divide both the numerator and the denominator by 5:
\[ \frac{85 \div 5}{30 \div 5} = \frac{17}{6} \]
Therefore, the final answer in simplest form is:
\[ \frac{17}{6} \]
Since \(\frac{17}{6}\) is an improper fraction, you can also express it as a mixed number:
\[ 2 \frac{5}{6} \]
Thus, the answer is:
\[ \frac{17}{6} \quad \text{or} \quad 2 \frac{5}{6} \]
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