Tính:1000/1009x2018/2019+19/2018x-2018/2019+1/2020

$\dfrac{1000}{1009}$ x $\dfrac{2018}{2019}$ + $\dfrac{19}{2018}$ x $\dfrac{-2018}{2019}$ + $\dfrac{1}{2020}$

= $\dfrac{1000.2018}{1009.2019}$ + $\dfrac{19.(-2018)}{2018.2019}$ + $\dfrac{1}{2000}$

= $\dfrac{1000.2}{1.2019}$ + $\dfrac{19.(-1)}{1.2019}$ + $\dfrac{1}{2000}$

= $\dfrac{2000}{2019}$ + $\dfrac{-19}{2019}$ + $\dfrac{1}{2000}$

= ($\dfrac{2000}{2019}$ + $\dfrac{-19}{2019}$) + $\dfrac{1}{2000}$

= $\dfrac{2000+(-19)}{2019}$ + $\dfrac{1}{2000}$

= $\dfrac{1981}{2019}$ + $\dfrac{1}{2000}$