$A=\dfrac{2020^3+1}{2020^2-2019}$
$=\dfrac{2020^3+1^3}{2020^2-2019}$
$=\dfrac{(2020+1)(2020^2-2020+1}{2020^2-2019}$
$=\dfrac{(2020+1)(2020^2-2019}{2020^2-2019}$
$=2020+1=2021$
$B=\dfrac{2020^3-1}{2020^2+2021}$
$=\dfrac{2020^3-1^3}{2020^2+2021}$
$=\dfrac{(2020-1)(2020^2+2020+1}{2020^2+2021}$
$=\dfrac{(2020-1)(2020^2+2021}{2020^2+2021}$
$=2020-1=2019$