Question

Help me!!!

Answer 1

Giải:

Ta có: \(A=\dfrac{2011+2012}{2012+2013}\)

\(=\dfrac{2011}{2012+2013}+\dfrac{2012}{2012+2013}\)

Áp dụng tính chất \(\dfrac{a}{b}>\dfrac{a}{b+m}\left(m>0\right)\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{2011}{2012}>\dfrac{2011}{2012+2013}\\\dfrac{2012}{2013}>\dfrac{2012}{2012+2013}\end{matrix}\right.\)

Cộng vế theo vế ta được:

\(B=\dfrac{2011}{2012}+\dfrac{2012}{2013}>\dfrac{2011}{2012+2013}\) \(+\dfrac{2012}{2012+2013}\)

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

Vậy \(A< B\)