\(N=3\dfrac{1}{117}\cdot\dfrac{1}{119}-\dfrac{4}{117}\cdot5\dfrac{118}{119}-\dfrac{5}{117\cdot119}+\dfrac{8}{39}\)
\(=\dfrac{1}{39}+\dfrac{1}{119}-\dfrac{4}{117}\cdot\dfrac{713}{119}-\dfrac{5}{\dfrac{117119}{1000}}+\dfrac{8}{39}\)
\(=\dfrac{1}{4641}-\dfrac{2852}{13923}-\dfrac{5000}{117119}+\dfrac{8}{39}\)
\(=-\dfrac{9827881}{232949691}\)