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-\frac{40}{72}-\frac{27}{72}
Least common multiple of 9 and 8 is 72. Convert -\frac{5}{9} and \frac{3}{8} to fractions with denominator 72.
\frac{-40-27}{72}
Since -\frac{40}{72} and \frac{27}{72} have the same denominator, subtract them by subtracting their numerators.
-\frac{67}{72}
Subtract 27 from -40 to get -67.