Question

so sanh A va B

A =\(\frac{2009}{2010}\) +\(\frac{2010}{2011}\)                                                             B =\(\frac{2009+2010}{2010+2011}\)

Answer 1

Ta có: \(\frac{2009}{2010}>\frac{2009}{2010+2011}\)  ; \(\frac{2010}{2011}>\frac{2010}{2011+2010}\)

\(\Rightarrow\frac{2009}{2010}+\frac{2010}{2011}>\frac{2009}{2010+2011}+\frac{2010}{2011+2010}=\frac{2009+2010}{2010+2011}\)

=> A > B

Answer 2

Ta có  \(\frac{2009}{2010}>\frac{2009}{2010+2011}\)           ,   \(\frac{2010}{2011}>\frac{2010}{2011+2010}\)

\(\Rightarrow\frac{2009}{2010}+\frac{2010}{2011}>\frac{2009}{2010+2011}+\frac{2010}{2011+2010}=\frac{2009+2010}{2010+2011}\)

\(\Rightarrow A>B\)