To solve this expression, we first need to find a common denominator for the fractions involved. The common denominator for 2/3 and 1/2021 is 3*2021 = 6063.

Now, we rewrite the expression with the common denominator:

2/3 + 2022/2021 - 2/3

Now, we can add and subtract the fractions:

(2*2021 + 2022 - 2*2021) / 6063
(4042 + 2022 - 4042) / 6063
2022 / 6063

Therefore, the final result is 2022/6063.