\(\dfrac{2011}{2010}< \dfrac{2011+1}{2010+1}=\dfrac{2012}{2011}\)

\(\Rightarrow\dfrac{2011}{2010}< \dfrac{2012}{2011}\)

\(\dfrac{2012}{2011}và\dfrac{2011}{2010}\\ \dfrac{2012}{2011}-1=\dfrac{1}{2011}\\ \dfrac{2011}{2010}-1=\dfrac{1}{2010}\\ \)

Vì \(\dfrac{1}{2011}< \dfrac{1}{2010}\\ \Rightarrow\dfrac{2012}{2011}< \dfrac{2011}{2010}\)

\(\dfrac{2012}{2011}\) = 1 + \(\dfrac{1}{2011}\);    \(\dfrac{2011}{2010}\) = 1 + \(\dfrac{1}{2010}\)

Vì \(\dfrac{1}{2011}\) < \(\dfrac{1}{2010}\)

Nên \(\dfrac{2012}{2011}\) < \(\dfrac{2011}{2010}\)

nghịch dảo 2 p/s ta có:

\(\frac{2010}{2009}v\text{à}\frac{2011}{2010}\)

\(\frac{2010}{2009}=1\frac{1}{2009}\)               ;\(\frac{2011}{2010}=1\frac{1}{2010}\)

   vì \(\frac{1}{2009}>\frac{1}{2010}\)

   =>\(\frac{2009}{2010}

1-\(\frac{2009}{2010}=\frac{2010}{2010}-\frac{2009}{2010}=\frac{1}{2010}\)

1-\(\frac{2010}{2011}=\frac{2011}{2011}-\frac{2010}{2011}=\frac{1}{2011}\)

Vì 2010 < 2011 nên \(\frac{1}{2010}>\frac{1}{2011}nên\frac{2009}{2010}>\frac{2010}{2011}\)

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

\(\dfrac{2010}{2011}\) và \(\dfrac{2011}{2012}\)

Ta có:

\(1-\dfrac{2010}{2011}=\dfrac{1}{2011}\)

\(1-\dfrac{2011}{2012}=\dfrac{1}{2012}\)

Vì \(\dfrac{1}{2011}>\dfrac{1}{2012}\) nên \(\dfrac{2010}{2011}< \dfrac{2011}{2012}\)

20112010​ và 2011201220122011​

Ta có:

1−20102011=120111−20112010​=20111​

1−20112012=120121−20122011​=20121​

Vì 12011>1201220111​>20121​ nên 20102011<2011201220112010​<20122011​

ta có: 1 - 2010/2011= 2011/2011 - 2010/2011=1/2011

           1 - 2011/2012= 2012/2012 - 2011/2012= 1/2012

   Vì 1/2011>1/2012

   Nên 2010/2011>2011/2012

\(\dfrac{2011}{2010}>1;\dfrac{2010}{2011}< 1\\ Nên:\dfrac{2011}{2010}>1>\dfrac{2010}{2011}\\ Vậy:\dfrac{2011}{2010}>\dfrac{2010}{2011}\)

                   Mình chỉ làm được câu a thôi!!!!

2010/2009 và 2011/2010

Ta có:

2010-1+1/2009=2009+1/2009=2009/2009+1/2009=1+1/2009

2011-1+1/2010=2010+1/2010=2010/2010+1/2010=1+1/2010

Vì  2009<2010=>1/2009>1/2010

=>1+1/2009>1+1/2010

=>2010/2009>2011/2010

Vậy 2010/2009>2011/2010

2010/2011 > 2009/2010

vì 1- 2010/2011=1/2011  

1- 2009/2010= 1/2010

1/2011 < 1/2010

nên 2010/2011 > 2009/2010

thật nhé không tin quy đồng

\(\dfrac{2011}{2010}=1-\dfrac{1}{2010}\)

\(\dfrac{97}{96}=1-\dfrac{1}{96}\)

mà -1/2010>-1/96

nên 2011/2010>97/96

\(\dfrac{2011}{2010}=1-\dfrac{1}{2010}\)

\(\dfrac{97}{96}=1-\dfrac{1}{96}\)

mà 1/2010<1/96

nên 2011/2010>97/96