\(=\dfrac{2^2-1+1}{\left(2-1\right)\left(2+1\right)}\cdot\dfrac{3^2-1+1}{\left(3-1\right)\left(3+1\right)}\cdot...\cdot\dfrac{2021^2-1+1}{\left(2021-1\right)\left(2021+1\right)}\)
\(=\dfrac{2}{1}\cdot\dfrac{3}{2}\cdot...\cdot\dfrac{2021}{2020}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot...\cdot\dfrac{2021}{2022}\)
\(=\dfrac{2021}{1}\cdot\dfrac{2}{2022}=\dfrac{2011}{1011}\)