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\frac{q-\left(8-\left(\frac{4}{12}+\frac{3}{12}\right)\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.
\frac{q-\left(8-\frac{4+3}{12}\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.
\frac{q-\left(8-\frac{7}{12}\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Add 4 and 3 to get 7.
\frac{q-\left(8-\frac{7\times 6}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Express \frac{7}{12}\times 6 as a single fraction.
\frac{q-\left(8-\frac{42}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Multiply 7 and 6 to get 42.
\frac{q-\left(8-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Reduce the fraction \frac{42}{12} to lowest terms by extracting and canceling out 6.
\frac{q-\left(\frac{16}{2}-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Convert 8 to fraction \frac{16}{2}.
\frac{q-\frac{16-7}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Since \frac{16}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{q-\frac{9}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Subtract 7 from 16 to get 9.
\frac{q-\frac{9}{2}}{8-\left(\frac{2}{6}+\frac{3}{6}\right)\times 6}
Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.
\frac{q-\frac{9}{2}}{8-\frac{2+3}{6}\times 6}
Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.
\frac{q-\frac{9}{2}}{8-\frac{5}{6}\times 6}
Add 2 and 3 to get 5.
\frac{q-\frac{9}{2}}{8-5}
Cancel out 6 and 6.
\frac{q-\frac{9}{2}}{3}
Subtract 5 from 8 to get 3.
\frac{q-\left(8-\left(\frac{4}{12}+\frac{3}{12}\right)\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Least common multiple of 3 and 4 is 12. Convert \frac{1}{3} and \frac{1}{4} to fractions with denominator 12.
\frac{q-\left(8-\frac{4+3}{12}\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Since \frac{4}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.
\frac{q-\left(8-\frac{7}{12}\times 6\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Add 4 and 3 to get 7.
\frac{q-\left(8-\frac{7\times 6}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Express \frac{7}{12}\times 6 as a single fraction.
\frac{q-\left(8-\frac{42}{12}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Multiply 7 and 6 to get 42.
\frac{q-\left(8-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Reduce the fraction \frac{42}{12} to lowest terms by extracting and canceling out 6.
\frac{q-\left(\frac{16}{2}-\frac{7}{2}\right)}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Convert 8 to fraction \frac{16}{2}.
\frac{q-\frac{16-7}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Since \frac{16}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{q-\frac{9}{2}}{8-\left(\frac{1}{3}+\frac{1}{2}\right)\times 6}
Subtract 7 from 16 to get 9.
\frac{q-\frac{9}{2}}{8-\left(\frac{2}{6}+\frac{3}{6}\right)\times 6}
Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.
\frac{q-\frac{9}{2}}{8-\frac{2+3}{6}\times 6}
Since \frac{2}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.
\frac{q-\frac{9}{2}}{8-\frac{5}{6}\times 6}
Add 2 and 3 to get 5.
\frac{q-\frac{9}{2}}{8-5}
Cancel out 6 and 6.
\frac{q-\frac{9}{2}}{3}
Subtract 5 from 8 to get 3.