Question

Simplify:

\[\left( \frac{3}{11} \times \frac{5}{6} \right) - \left( \frac{9}{12} \times \frac{4}{3} \right) + \left( \frac{5}{13} \times \frac{6}{15} \right)\]

Answer 1

\[(\frac{3}{11} \times \frac{5}{6}) - (\frac{9}{12} \times \frac{4}{3}) + (\frac{5}{13} \times \frac{6}{15})\]
\[ = \frac{5}{22} - 1 + \frac{2}{13}\]
\[ = \frac{5 \times 13 - 286 + 2 \times 22}{286}\]
\[ = \frac{65 - 286 + 44}{286}\]
\[ = \frac{- 177}{286}\]