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\frac{93}{18}-\frac{68}{18}
Least common multiple of 6 and 9 is 18. Convert \frac{31}{6} and \frac{34}{9} to fractions with denominator 18.
\frac{93-68}{18}
Since \frac{93}{18} and \frac{68}{18} have the same denominator, subtract them by subtracting their numerators.
\frac{25}{18}
Subtract 68 from 93 to get 25.