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-\frac{16}{30}-\frac{25}{30}
Least common multiple of 15 and 6 is 30. Convert -\frac{8}{15} and \frac{5}{6} to fractions with denominator 30.
\frac{-16-25}{30}
Since -\frac{16}{30} and \frac{25}{30} have the same denominator, subtract them by subtracting their numerators.
-\frac{41}{30}
Subtract 25 from -16 to get -41.