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\(A=\frac{2015^{2014}+1}{2015^{2014}-1}=\frac{2015^{2014}-1+2}{2015^{2014}-1}=1+\frac{2}{2015^{2014}-1}.\)
\(B=\frac{2015^{2014}-1}{2015^{2014}-3}=\frac{2015^{2014}-3+2}{2015^{2014}-3}=1+\frac{2}{2015^{2014}-3}\)
mà \(\frac{2}{2015^{2014}-1}< \frac{2}{2015^{2014}-3}\)( 20152014 -1 > 20152014 - 3)
\(\Rightarrow A< B\)
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Vì 2017<2018 nên\(\frac{1}{2017}\)>\(\frac{1}{2018}\)
⇒\(\frac{2}{2017}\)>\(\frac{1}{2018}\)
⇒\(\frac{2015}{2017}\)=1-\(\frac{2}{2017}\)<1-\(\frac{1}{2018}\)=\(\frac{2017}{2018}\)
Vậy, \(\frac{2015}{2017}\)< \(\frac{2017}{2018}\)
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a = \(\frac{2013}{2014}+\frac{2014}{2015}=\frac{2014-1}{2014}+\frac{2015-1}{2015}\)
\(=1-\frac{1}{2014}+1-\frac{1}{2015}\)
\(=2-\left(\frac{1}{2014}+\frac{1}{2015}\right)>1\) (1)
b = \(\frac{2013+2014}{2014+2015}
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