Ta có: \(\frac{2012}{2011}=1-\frac{1}{2011}\)

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

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

\(\Rightarrow\frac{2012}{2011}>\frac{2011}{2010}\)

\(\frac{2012}{2011}=1+\frac{1}{2011}\)
\(\frac{2011}{2010}=1+\frac{1}{2010}\)
vì  \(\frac{1}{2011}< \frac{1}{2010}\)
nên \(\frac{2012}{2011}< \frac{2011}{2010}\)

Ta có: 2012/2011 - 1 = 1/2011

          2011/2010 - 1 = 1/2010

Vì 1/2011 <1/2010 => 2012/2011 > 2011/2010.

#)Giải :

Ta có : \(1-\frac{2010}{2011}=\frac{1}{2011}\)

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

Vì \(\frac{1}{2011}>\frac{1}{2012}\Rightarrow\frac{2010}{2011}>\frac{2011}{2012}\)

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

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

\(2011\)<\(2012\)\(\Rightarrow\frac{1}{2011}\)>\(\frac{1}{2012}\)

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

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

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

vì \(\frac{1}{2011}>\frac{1}{2012}\)nên \(\frac{2010}{2011}< \frac{2011}{2012}\)

a) \(1=\frac{45}{46}+\frac{1}{46}\)

    \(1=\frac{2011}{2012}+\frac{1}{2012}\)

Vì \(\frac{1}{46}>\frac{1}{2012}\)\(\Rightarrow\)\(\frac{45}{46}< \frac{2011}{2012}\)

b)Vì 2010/2011 < 1 và 17/16 > 1 => 2010/2011 < 17/16

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

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

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

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

Ai phúp tui làm -49 phần 211 và 13 phần 1999 

Và bài 311 phần 256 và 199 và 203 

26 phần 27 và 96 phần 97

\(A=\dfrac{-9\cdot10+\left(-19\right)}{10^{2011}}=\dfrac{-28}{10^{2011}}\)

\(B=\dfrac{-9\cdot10-19}{10^{2011}}=\dfrac{-109}{10^{2011}}\)

=>A>B

+ta có 10^2010=10...0(2010 số 0)

và 10^2011=10...0(2011 số 0)

suy ra  -9/10...0(2010 số 0)= -90/10...0(2011 số 0)[nhân tử,mẫu cho 10]

suy ra A=-90/10...0(2011 số 0)+-19/10...0(2011 số 0)= -109/10...0(2011 số 0)     [1]

+-19/10...0(2010 số 0)= -190/10...0(2011 số 0)[nhân tử,mẫu cho 10]

và 10^2011=10...0(2011 số 0)

suy ra -9/10...0(2011 số 0)+-190/10...0(2011 số 0)= -199/10...0(2011 số 0)    [2]

vì -109>-199 suy ra [1]>[2]

K CHO MIK VS BẠN ƠIIIIIIIIIIIIIIIIIII

\(-A=\frac{9}{10^{2010}}+\frac{19}{10^{2011}}\)

\(-A=\frac{9}{10^{2010}}+\frac{10}{10^{2011}}+\frac{9}{10^{2011}}\)

\(-A=\frac{9}{10^{2010}}+\frac{1}{10^{2010}}+\frac{9}{10^{2011}}\)

\(-A=\frac{10}{10^{2010}}+\frac{9}{10^{2011}}\)

\(-A=\frac{1}{10^{2009}}+\frac{9}{10^{2011}}\)

\(-B=\frac{9}{10^{2011}}+\frac{19}{10^{2010}}\)

Làm tương tự nhé 

ta thấy -b > -a nên a>b