a) \(\frac{31}{17}+\frac{-5}{13}+\frac{-8}{13}-\frac{14}{17}\)
\(=\left(\frac{31}{17}-\frac{14}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)\)
\(=1+\left(-1\right)\)
\(=0\)
b) \(\frac{-5}{7}.\frac{2}{11}+\frac{-5}{7}.\frac{9}{11}+\frac{5}{7}\)
\(=\frac{-5}{7}.\left(\frac{2}{11}+\frac{9}{11}\right)+\frac{5}{7}\)
\(=\frac{-5}{7}.1+\frac{5}{7}\)
\(=\frac{-5}{7}+\frac{5}{7}\)
\(=0\)