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-\frac{3}{18}-\frac{10}{18}
Least common multiple of 6 and 9 is 18. Convert -\frac{1}{6} and \frac{5}{9} to fractions with denominator 18.
\frac{-3-10}{18}
Since -\frac{3}{18} and \frac{10}{18} have the same denominator, subtract them by subtracting their numerators.
-\frac{13}{18}
Subtract 10 from -3 to get -13.