\(B=\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}

\(A=\frac{2011}{2012}+\frac{2012}{2013}\)  \(và\)   \(B=\frac{2011+2012}{2012+2013}\)

\(Ta\)    \(có\) \(:\)   \(B=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)

                     \(B=\frac{2011}{4025}+\frac{2012}{4025}\)

\(Vì\)    \(\frac{2011}{2012}>\frac{2011}{4025}và\frac{2012}{2013}>\frac{2012}{4025}\)

\(Nên\)  \(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{4025}+\frac{2012}{4025}\)

\(Vậy\)   \(A=\frac{2011}{2012}+\frac{2012}{2013}>B=\frac{2011+2012}{2012+2013}\)

A = \(\frac{2011}{2012}+\frac{2012}{2013}=1,999006211\)

B=\(\frac{2011+2012}{2012+2013}=\frac{4023}{4025}\)

Mà \(\frac{4023}{4025}< 1,999006211\) vì  4023/4025 nhỏ hơn 1 (cách tính nhanh )

Nên A>B

TA CÓ :

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

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

VÌ : \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)

\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)

\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)

=> A > B 

VẬY , A > B

Mình tự hỏi. sao banh biết rồi còn đăng lên làm gì??????????

CÁCH CỦA MÌNH LÀ HOÀN TOÀN ĐÚNG NHA !

$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$

$\frac{\frac{2010}{2011}}{\frac{2012}{2013}}+\frac{\frac{2011}{2012}}{\frac{2013}{2014}}+\frac{\frac{2012}{2013}}{\frac{2014}{2015}}$

$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$

$\frac{\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}}{\frac{2012+2013+2014}{2013+2014+2015}}$

$\frac{\frac{2010+2011+2012}{2011+2012+2013}}{\frac{2012}{2013}+\frac{2013}{2014}+\frac{2014}{2015}}$

dễ ợt nhưng éo biết làm thông cảm nha

ban Dang Ha Trang an noi gi ki vay 

A = \(\frac{2011+2012}{2012+2013}=\frac{2011+2012}{4025}\)

Ta có:

\(\frac{2011}{2012}>\frac{2011}{4025}\)

\(\frac{2012}{2013}>\frac{2012}{4025}\)

=> \(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{4025}+\frac{2012}{4025}\)

=> \(B>\frac{2011+2012}{4025}\)

=>\(B>A\)

bạn xem ở đây nhé

Đây

A = B

mình giỏi lắm

IQ vô cực

Ta có \(B=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}\)

    Lại có: \(\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}\)                        ( ngoặc 2 dòng này lại nhé dòng này và dòng trên)

 \(\Rightarrow B>A\)

nhầm là A > B

Gọi 2011 là a

2012 là b;2013 là c

=>\(A=\frac{2011}{2012}+\frac{2012}{2013}=\frac{a}{b}+\frac{b}{c}\);\(B=\frac{2011+2013}{2012+2013}=\frac{a+c}{b+c}\)

=>\(A=\frac{a}{b}+\frac{b}{c}=\frac{ac+b^2}{bc}\)\(=\frac{\left(ac+b^2\right).\left(b+c\right)}{bc.\left(b+c\right)}\);\(B=\frac{a+c}{b+c}=\frac{\left(a+c\right).bc}{bc.\left(b+c\right)}\)

b+c>a+c;b²+ac>bc

Vậy A>B

?????????????????????????????????

 Cách 1

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

\(A=\frac{2011+1}{1+2013}\)

\(A=\frac{2012}{2014}\)

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

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

\(B=\frac{2011+1}{1+2013}\)

\(B=\frac{2012}{2014}\)

Vậy A và B bằng nhau vì cùng bằng \(\frac{2012}{2014}\)

Cách 2

A và B bằng nhau vì đều có hai phân số 2011/2012 + 2012/2013

Ta có: \(\frac{2011}{2012}>\frac{2011}{2012+2013}\)

\(\frac{2012}{2013}>\frac{2012}{2012+2013}\)

\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}=\frac{2011+2012}{2012+2013}\)

Vậy A < B

ta có: \(\frac{2011}{2012}>\frac{2011}{2012+2013};\frac{2012}{2013}>\frac{2012}{2013+2012}.\)

\(\Rightarrow A>\frac{2011}{2012+2013}+\frac{2012}{2013+2012}=\frac{2011+2012}{2012+2013}=B\)

....

Ta có \(\frac{2011}{2012}>\frac{2011}{2012+2013}\)

          \(\frac{2012}{2013}>\frac{2012}{2012+2013}\)

CỘNG VẾ THEO VẾ,TA CÓ:

\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)

\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011+2012}{2012+2013}\)

\(\Rightarrow A>B\)

Vậy A>B

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

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

Mà \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)

       \(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)

      \(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)

Cộng vế theo vế, ta có : \(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\)

\(\Rightarrow P>Q\)

Ta có:

2010/2011 >2010/2011+2012+2013. ;2011/2012 >2011/2011+2012+2013 .;2012/2013 >2012/2011+2012+2013 ->2010/2011+2011/2012+2012/2013 >2010+2011+2012/2011+2012+2013. Vậy P > Q

thanks các bạn nhìu nha