Question - Simplifying a Fractional Expression

\[ 6 \left( \frac{2}{3} \times \frac{4}{7} - \frac{1}{2} \right) + \frac{5}{6} \times \frac{7}{5} \]

\[ = 6 \left( \frac{8}{21} - \frac{1}{2} \right) + \frac{35}{30} \]

\[ = 6 \left( \frac{8}{21} - \frac{10.5}{21} \right) + \frac{7}{6} \]

\[ = 6 \left( -\frac{2.5}{21} \right) + \frac{7}{6} \]

\[ = -\frac{15}{21} + \frac{7}{6} \]

\[ = -\frac{5}{7} + \frac{7}{6} \]

\[ = -\frac{30}{42} + \frac{49}{42} \]

\[ = \frac{19}{42} \]