Ta có : \(\frac{x+1}{2017}+\frac{x+1}{2016}=\frac{x+1}{2015}+\frac{x+1}{2014}\)
\(\Rightarrow\frac{x+1}{2017}+\frac{x+1}{2016}-\frac{x+1}{2015}-\frac{x+1}{2014}=0\)
\(\Rightarrow\left(x+1\right)\left(\frac{1}{2017}+\frac{1}{2016}-\frac{1}{2015}-\frac{1}{2014}\right)=0\)
Vì \(\left(\frac{1}{2017}+\frac{1}{2016}-\frac{1}{2015}-\frac{1}{2014}\right)\ne0\)
Nên : x + 1 = 0
=> x = -1
Vậy x = -1 .