\(a,-\dfrac{2}{7}.\left(\dfrac{5}{13}-\dfrac{9}{15}\right)-\dfrac{2}{7}.\dfrac{8}{13}\)
\(b,\dfrac{1}{10}.\dfrac{4}{11}+\dfrac{1}{10}.\dfrac{8}{11}-\dfrac{1}{10}.\dfrac{1}{11}\)
\(c,\left(\dfrac{19}{68}-\dfrac{11}{22}+\dfrac{16}{31}\right).\left(1-\dfrac{1}{2}-\dfrac{1}{2}\right)\)
\(d,\left(1-\dfrac{1}{2}\right).\left(1-\dfrac{1}{3}\right).\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2010}\right)\)
\(a,-\dfrac{2}{7}\cdot\left(\dfrac{5}{13}-\dfrac{9}{15}\right)-\dfrac{2}{7}\cdot\dfrac{8}{13}\\ =-\dfrac{2}{7}\cdot\left(\dfrac{5}{13}-\dfrac{9}{15}+\dfrac{8}{13}\right)\\ =-\dfrac{2}{7}\cdot\left(1-\dfrac{9}{15}\right)\\ =-\dfrac{2}{7}\cdot\dfrac{6}{15}\\ =-\dfrac{2}{7}\cdot\dfrac{2}{5}\\ =\dfrac{-4}{35}\\ b.\dfrac{1}{10}\cdot\dfrac{4}{11}+\dfrac{1}{10}\cdot\dfrac{8}{11}-\dfrac{1}{10}\cdot\dfrac{1}{11}\\ =\dfrac{1}{10}\cdot\left(\dfrac{4}{11}+\dfrac{8}{11}-\dfrac{1}{11}\right)\\ =\dfrac{1}{10}\cdot\dfrac{11}{11}\\ =\dfrac{1}{10}\cdot1\\ =\dfrac{1}{10}\\ c.\left(\dfrac{19}{68}-\dfrac{11}{12}+\dfrac{16}{31}\right)\cdot\left(1-\dfrac{1}{2}-\dfrac{1}{2}\right)\\ =\left(\dfrac{19}{68}-\dfrac{11}{12}+\dfrac{16}{31}\right)\cdot\left(1-1\right)\\ =\left(\dfrac{19}{68}-\dfrac{11}{12}+\dfrac{16}{31}\right)\cdot0\\ =0\\ d.\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)...\left(1-\dfrac{1}{2010}\right)\\ =\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2009}{2010}\\ =\dfrac{2\cdot3\cdot4\cdot...\cdot2009}{\left(2\cdot3\cdot4\cdot...\cdot2009\right)\cdot2010}\\ =\dfrac{1}{2010}\)
