\(A=\frac{2014^{2015}+2}{2014^{2016}+9}\)
\(2014A=\frac{2014\left(2014^{2015}+2\right)}{2014^{2016}+9}=\frac{2014^{2016}+4028}{2014^{2016}+9}=\frac{\left(2014^{2016}+9\right)+4019}{2014^{2016}+9}=\frac{2014^{2016}+9}{2014^{2016}+9}+\frac{4019}{2014^{2016}+9}=1+\frac{4019}{2014^{2016}+9}\)
\(B=\frac{2014^{2016}+2}{2014^{2017}+9}\)
\(2014B=\frac{2014\left(2014^{2016}+2\right)}{2014^{2017}+9}=\frac{2014^{2017}+4028}{2014^{2017}+9}=\frac{2014^{2017}+9+4019}{2014^{2017}+9}=\frac{2014^{2017}+9}{2014^{2017}+9}+\frac{4019}{2014^{2017}+9}=1+\frac{4019}{2014^{2017}+9}\)
Ta thấy:
\(2014^{2016}+9< 2014^{2017}+9\)
\(\Rightarrow\frac{4019}{2014^{2016}+9}>\frac{4019}{2014^{2017}+9}\)
\(\Rightarrow1+\frac{4019}{2014^{2016}+9}>1+\frac{4019}{2014^{2017}+9}\)
\(\Rightarrow A>B\)
Vậy ....
