ta có : 

\(B=\frac{2010+2011}{2011+2012}=\frac{2010}{2011+2012}+\frac{2011}{2011+2012}\)

ta có : \(\frac{2010}{2011}>\frac{2010}{2011+2012}\)

            \(\frac{2011}{2012}>\frac{2011}{2011+2012}\)

=> \(\frac{2010}{2011}+\frac{2011}{2012}>\frac{2010+2011}{2011+2012}\)

hay A>B

Có : \(2009+2010>\dfrac{2009}{2010}\) ; \(2011+2012>\dfrac{2011}{2012}\)

\(\dfrac{2011}{2010}>1\) ; \(\dfrac{2010}{2011}< 1\) \(\Rightarrow\dfrac{2011}{2010}>\dfrac{2010}{2011}\)

Ta có : \(2009+2010+\dfrac{2011}{2010}+2011+2012>\dfrac{2009}{2010}+\dfrac{2010}{2011}+\dfrac{2011}{2012}\)

\(\Leftrightarrow B>A\)

Hay \(A< B\)

Ta có: \(\frac{2010}{2011}>\frac{2010}{2011+2012}\)

\(\frac{2011}{2012}>\frac{2011}{2011+2012}\)

Nên \(\frac{2010}{2011}+\frac{2011}{2012}>\frac{2010+2011}{2011+2012}\)\(\Rightarrow A>B\)

So sánh: \(\frac{2010}{2011}+\frac{2011}{2012}\) với \(\frac{2010+2011}{2011+2012}\)

Sao hông thêm 2 cái nữa cho tròn 440 luôn

Lời giải:

$A=1-\frac{1}{2011}+1-\frac{1}{2012}+1+\frac{2}{2010}$

$=3+(\frac{1}{2010}-\frac{1}{2011})+(\frac{1}{2010}-\frac{1}{2012})$

$> 3+0+0+0=3$

Ta có đpcm.

\(P=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}=\frac{2010}{8144863716}+\frac{2011}{8144863716}+\frac{2012}{8144863716}\)

\(=\frac{6033}{8144863716}=\frac{1}{1350052}\)

\(Q=2010+2011+\frac{2012}{2011}+2012+2013\)

\(=2010+2011+2012+2013+\frac{2012}{2011}\)

\(=8046+\frac{2012}{2011}=\frac{8046}{1}+\frac{2012}{2011}\)

\(=\frac{16180506}{2011}+\frac{2012}{2011}=\frac{16182518}{2011}\)

ai giải dùm vs

a=b

l-i-k-e cho mình nha

a=b                                               

\(\frac{2010+2011+2012}{2011+2012+2013}=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)

Vì \(\frac{2010}{2011+2012+2013}<\frac{2010}{2011};\frac{2011}{2011+2012+2013}<\frac{2011}{2012};\frac{2012}{2011+2012+2013}<\frac{2012}{2013}\)

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