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Ta có:
\(A=\frac{2021^{2021}+1}{2021^{2022}+1}\Leftrightarrow10A=\frac{2021^{2022}+10}{2021^{2022}+1}=1+\frac{9}{2021^{2022}+1}\)
\(B=\frac{2021^{2022}-1}{2021^{2023}-1}\Leftrightarrow10B=\frac{2021^{2023}-10}{2021^{2023}-1}=1-\frac{9}{2021^{2023}-1}\)
Hay ta đang so sánh: \(\frac{9}{2021^{2022}};\frac{9}{2021^{2023}}\)
Mà \(\frac{9}{2021^{2022}}>\frac{9}{2021^{2023}}\)nên \(\frac{2021^{2021}+1}{2021^{2022}+1}>\frac{2021^{2022}-1}{2021^{2023}-1}\)hay\(A>B\)
Vậy \(A>B\)

Nhỏ hơn
Ta có 2020/2021 <1
2021/2022 <1
2022/2023 <1
2023/2024 <1
Suy ra A=(2021/2021+2021/2022 +2022/2023 +2023/2024) < (1+1+1+1)= 4
Vậy A <4
Chúc bạn học tốt
\(\dfrac{2020}{2021}< 1\)
\(\dfrac{2021}{2022}< 1\)
\(\dfrac{2021}{2022}< 1\)
\(\dfrac{2023}{2024}< 1\)
Do đó: A<4

A = ( 2022 x 0,75 + 2022 : 4) - ( 2021 : 0,1 : 10)
= (2022 x 0,75 + 2022 x 0,25) - ( 2021 : 1/10 : 10)
= 2022 x(0,75+0,25) - 2021x 10 : 10
= 2022x 1 - 2021
= 2022 - 2021
=1


Không cần tính, ta thấy : 2022/2021 > 2021/2022
Vậy : 2022/2021*2023 > 2021/2022*2022

Bài 1:
A = 1996 x 1997 x 1998 x 1999 + 2021 x 2022 x 2023 x 2024
A = (1996 x 1997) x (1998 x 1999) + (2021 x 2022) x (2023 x 2024)
A = \(\overline{..2}\) x \(\overline{..2}\) + \(\overline{..2}\) x \(\overline{..2}\)
A = \(\overline{..4}\) + \(\overline{..4}\)
A = \(\overline{..8}\)

\(\dfrac{2022}{2021}=\dfrac{2022}{2021}-1=\dfrac{1}{2021}< \dfrac{2021}{2020}-1=\dfrac{1}{2020}=\dfrac{2021}{2020}\)
\(=>\dfrac{2022}{2021}< \dfrac{2021}{2020}\)


giúp mình với tối nay mình nộp bài cho cô rồi
A = \(\frac49\) x \(\frac{2021}{2022}\) + \(\frac{2021}{2022}\) x \(\frac{10}{9}\) - \(\frac{2021}{2022}\) x \(\frac59\)
A = \(\frac{2021}{2022}\) x (\(\frac49\) + \(\frac{10}{9}\) - \(\frac59\))
A = \(\frac{2021}{2022}\) x (\(\frac{14}{9}-\frac59\))
A = \(\frac{2021}{2022}\) x 1
A = \(\frac{2021}{2022}\) `