\(\dfrac{1}{2}+\dfrac{-1}{5}+\dfrac{-5}{7}+\dfrac{1}{6}+\dfrac{-3}{35}+\dfrac{1}{3}\)
\(=\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{-1}{5}+\dfrac{-5}{7}-\dfrac{3}{35}\right)\)
\(=\dfrac{3+2+1}{6}+\dfrac{-7-25-3}{35}\)
\(=\dfrac{6}{6}-\dfrac{35}{35}\)
=1-1
=0