\[1\frac{5}{14} - \left( 2\frac{2}{13} - 8\frac{9}{14} \right) =\]
\[= 1\frac{5}{14} - 2\frac{2}{13} + 8\frac{9}{14} =\]
\[= 9\frac{14}{14} - 2\frac{2}{13} = 10 - 2\frac{2}{13} =\]
\[= 9\frac{13}{13} - 2\frac{2}{13} = 7\frac{11}{13}.\]