\(\frac{2008\cdot2009+4018}{2010\cdot2011-4020}=\frac{2008\cdot2009+2009\cdot2}{2010\cdot2011-2010\cdot2}=\frac{\left(2008+2\right)\cdot2009}{2010\left(2011-2\right)}=\frac{2010\cdot2009}{2010\cdot2009}=1\)

b

2008.2009 + 4018 = 2008.2009 + 2.2009 0.25

= 2009.(2008+2) = 2009.2010 0.25

2010.2011-4020 = 2010.2011-2.2010 0.25

= 2010.(2011-2) = 2010.2009 0.25

⇒2008.2009 4018

2010.2011 4020

+

−

= 1

Ta co:\(\frac{2008.2009+4018}{2010.2011-4020}=\frac{2008.\left(2011-2\right)+4018}{\left(2008+2\right).2011-4020}\)

\(=\frac{2008.2011-2008.2+4018}{2008.2011+2011.2-4020}=\frac{2008.2011+4018-4016}{2008.2011+4022-4020}\)

\(=\frac{2008.2011+2}{2008.2011+2}=1\)

2008.2009+4018

=2008.2009+2009.2

=2009.(2008+2)

=2009.3000

=6027000

b.2010.2011+4020

=2010.2011+2010.2

=2010.(2011+2)

=2010.2013

=4046130

2008 x 2009 + 40 18

= 4034072 + 4018

 = 4038090

2010 x 2011 + 4020

= 4042110 + 4020

= 4046130

( 2008 + 1009 ) . ( 2009 - 1009 ) + 4018

3017 . 1000 + 4018

3017000 + 4018

3021018

2008.2009+4018/2010.2011-4020

=2008.2009+2009.2/2010.2011-2010.2

=2009.(2008+2)/2010.(2011-2)

=2009.2010/2010.2009

=1

                                   Bài làm :

Ta có :

\(A=\frac{2008.2009+4018}{2010.2011-4020}\)

\(A=\frac{2008.2009+2009.2}{2010.2011-2010.2}\)

\(A=\frac{2009.\left(2008+2\right)}{2010.\left(2011-2\right)}\)

\(A=\frac{2009.2010}{2010.2009}=1\)

Vậy A=1 .

Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

\(A=\frac{2008.2009+4018}{2010.2011-4020}\)

\(A=\frac{2008.2009+2009.2}{2010.2011-2010.2}\)

\(A=\frac{2009.\left(2008+2\right)}{2010.\left(2011-2\right)}\)

\(A=\frac{2009.2010}{2010.2009}=1\)

Vậy ....

Ta có : 

\(B=\frac{2008+2009+2010}{2009+2010+2011}=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)

Vì : 

\(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)

\(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)

\(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)

Nên \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)

\(\Rightarrow\)\(A>B\)

Vậy \(A>B\)

Ta có: \(B=\frac{2008+2009+2010}{2009+2010+2011}\)

                  \(=\frac{2008}{2009+2010+2011}+\frac{2009}{2009+2010+2011}+\frac{2010}{2009+2010+2011}\)

Vì \(\frac{2008}{2009}>\frac{2008}{2009+2010+2011}\)

    \(\frac{2009}{2010}>\frac{2009}{2009+2010+2011}\)

   \(\frac{2010}{2011}>\frac{2010}{2009+2010+2011}\)

nên \(\frac{2008}{2009}+\frac{2009}{2010}+\frac{2010}{2011}>\frac{2008+2009+2010}{2009+2010+2011}\)

hay A > B

Vậy A > B 

\(B=\dfrac{2008+2009+2010}{2009+2010+2011}=\dfrac{2008}{2009+2010+2011}+\dfrac{2009}{2009+2010+2011}+\dfrac{2010}{2009+2010+2011}\)Ta có : \(\dfrac{2008}{2009}>\dfrac{2008}{2009+2010+2011}\)

\(\dfrac{2009}{2010}>\dfrac{2009}{2009+2010+2011}\)

\(\dfrac{2010}{2011}>\dfrac{2010}{2009+2010+2011}\)\(=>\dfrac{2008}{2009}+\dfrac{2009}{2010}+\dfrac{2010}{2011}>\dfrac{2008+2009+2010}{2009+2010+2011}\)

Hay A > B

bằng nhau bạn nhé