\(1-\dfrac{2019\times2022-2000}{2019\times2021+19}\)
\(\Rightarrow1-\dfrac{2019\times\left(2020+2\right)-2000}{2019\times\left(2020+1\right)+19}\)
\(=1-\dfrac{2019\times2020+2019\times2-2000}{2019\times2020+2019+19}\)
\(=1-\dfrac{2019\times2020+4038-2000}{2019\times2020+2038}\)
\(=1-\dfrac{2019\times2020+2038}{2019\times2020+2038}=1-1=0\)