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\frac{3}{6}+\frac{4}{6}-\left(-\frac{1\times 6+1}{6}\right)
Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.
\frac{3+4}{6}-\left(-\frac{1\times 6+1}{6}\right)
Since \frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.
\frac{7}{6}-\left(-\frac{1\times 6+1}{6}\right)
Add 3 and 4 to get 7.
\frac{7}{6}-\left(-\frac{6+1}{6}\right)
Multiply 1 and 6 to get 6.
\frac{7}{6}-\left(-\frac{7}{6}\right)
Add 6 and 1 to get 7.
\frac{7}{6}+\frac{7}{6}
The opposite of -\frac{7}{6} is \frac{7}{6}.
\frac{7+7}{6}
Since \frac{7}{6} and \frac{7}{6} have the same denominator, add them by adding their numerators.
\frac{14}{6}
Add 7 and 7 to get 14.
\frac{7}{3}
Reduce the fraction \frac{14}{6} to lowest terms by extracting and canceling out 2.