2021 Fall AMC 10B Problem 3

We can rewrite this as $$\dfrac{2021\cdot 2021}{2020\cdot 2021} -\dfrac{2020\cdot 2020}{2020\cdot 2021}$$ $$= \dfrac{2021^2-2020^2}{2020\cdot 2021}.$$ This can be simplified to $$\dfrac{(2021-2020)(2021+2020)}{2020\cdot 2021}$$ $$=\dfrac{4041}{2020\cdot 2021}.$$ Since $4041$ is coprime with both $2020$ and $2021,$ we know $4041$ is the numerator. Thus, the answer is E .