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\frac{15}{18}-\frac{16}{18}
Least common multiple of 6 and 9 is 18. Convert \frac{5}{6} and \frac{8}{9} to fractions with denominator 18.
\frac{15-16}{18}
Since \frac{15}{18} and \frac{16}{18} have the same denominator, subtract them by subtracting their numerators.
-\frac{1}{18}
Subtract 16 from 15 to get -1.