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 !

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

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

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

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

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

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

dễ ợt nhưng éo biết làm thông cảm nha

ban Dang Ha Trang an noi gi ki vay 

Ta có

\(\frac{A^{2011}}{A^{2012}}=\frac{A^{2012}}{A^{2103}}=\frac{A}{A^2}\)

=> \(\frac{A^{2011}}{A^{2012}}+\frac{A^{2012}}{A^{2013}}=\frac{2A}{A^2}\)

\(\frac{A^{2011+2012}}{A^{2012+2013}}=\frac{A^{4023}}{A^{4025}}=\frac{1}{A^2}\)

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

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

Tách A ra thành 2 phân số cùng tử(dễ thôi).

So sánh mỗi phân số với 1 phân số tương ứng ở B.

=>A<B.

Vậy A<B.

Ta có :

\(B=\frac{1011}{2012+2013}\)+\(\frac{2012}{2012+2013}\)=\(\frac{2011+2012}{2012+2013}\)

Vì:

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

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

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

Vậy A <B

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

câu này khó quá mk chịu

Tất nhiên là A < B rồi 

cậu tra trên mạng í lắm lắm

Cả hai số bằng nhau

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

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

Vậy A  > B 

Ta có :

A=\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\left(1\right)\)

B=\(\frac{2011}{2012}+\frac{2012}{2013}\left(2\right)\)

Từ (1) và (2) suy ra A<B

Đầu tiên:

Ta có:

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

Vì:

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

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

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

Vậy B>A