\(\dfrac{1}{2}.\dfrac{1}{-3}-\dfrac{1}{3}.\dfrac{1}{4}+\dfrac{1}{4}.\dfrac{1}{-5}-\dfrac{1}{5}.\dfrac{1}{6}=\dfrac{-1}{3}\left(\dfrac{1}{2}+\dfrac{1}{4}\right)+\dfrac{-1}{5}\left(\dfrac{1}{4}+\dfrac{1}{6}\right)=\dfrac{-1}{3}.\dfrac{3}{4}+\dfrac{-1}{5}.\dfrac{5}{12}=\dfrac{-1}{4}+\dfrac{-1}{12}=\dfrac{-4}{12}=\dfrac{-1}{3}\)
`1/2 . 1/[-3]-1/3 . 1/4+1/4 . 1/[-5]-1/5 . 1/6`
`=-1/3 . 1/2-1/3 . 1/4-1/5 . 1/4-1/5 . 1/6`
`=(-1/3 . 1/2-1/3 . 1/4)+(-1/5 . 1/4-1/5 . 1/6)`
`=-1/3 .(1/2+1/4)-1/5 .(1/4+1/6)`
`=-1/3 . 3/4-1/5 . 5/12`
`=-1/4-1/12`
`=-1/3`