\(a)\dfrac{2}{3}+\dfrac{-5}{12}\\ =\dfrac{8}{12}+\dfrac{-5}{12}\\ =\dfrac{3}{12}\\ =\dfrac{1}{4}\\ b)\dfrac{2}{5}-\dfrac{5}{6}+\dfrac{3}{5}+\dfrac{11}{6}\\ =\left(\dfrac{2}{5}+\dfrac{3}{5}\right)+\left(\dfrac{11}{6}-\dfrac{5}{6}\right)\\ =\dfrac{5}{5}+\dfrac{6}{6}\\ =1+1=2\\ c)\dfrac{5}{7}\cdot\dfrac{5}{11}+\dfrac{5}{7}\cdot\dfrac{2}{11}-\dfrac{14}{11}\cdot\dfrac{5}{7}\\ =\dfrac{5}{7}\cdot\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\\ =\dfrac{5}{7}\cdot\dfrac{-7}{11}\\ =-\dfrac{5}{11}\\ d)\left(4-\dfrac{5}{12}\right):\dfrac{43}{36}+\dfrac{5}{24}\\ =\dfrac{43}{12}\cdot\dfrac{36}{43}+\dfrac{5}{24}\\ =3+\dfrac{5}{24}\\ =\dfrac{77}{24}\\ e)\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\\ =\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\\ =\dfrac{1}{2}-\dfrac{1}{7}\\ =\dfrac{5}{14}\)
