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34 x 34 > 35 x 33
107 x 108 > 106 x 109
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\(\frac{2015^{35}+1}{2015^{34}+1}=\frac{2015^{35}+2015-2014}{2015^{34}+1}=\frac{2015\left(2015^{34}+1\right)-2014}{2015^{34}+1}=\frac{2015\left(2015^{34}+1\right)}{2015^{34}+1}-\frac{2014}{2015^{34}+1}=2015-\frac{2014}{2015^{34}+1}\)
\(\frac{2015^{34}+1}{2015^{33}+1}=\frac{2015^{34}+2015-2014}{2015^{33}+1}=\frac{2015\left(2015^{33}+1\right)-2014}{2015^{33}+1}=\frac{2015\left(2015^{33}+1\right)}{2015^{33}+1}-\frac{2014}{2015^{33}+1}=2015-\frac{2014}{2015^{33}+1}\)
Mà \(2015-\frac{2014}{2015^{34}+1}>2015-\frac{2014}{2015^{33}+1}\)
Vậy\(\frac{2015^{35}+1}{2015^{34}+1}>\frac{2015^{34}+1}{2015^{33}+1}\)