\(2016x+x\frac{1}{2016}-2016=\frac{1}{2016}\)
\(\Rightarrow2016x-2016+x.\frac{1}{2016}-\frac{1}{2016}=0\)
\(\Rightarrow2016.\left(x-1\right)+\frac{1}{2016}.\left(x-1\right)=0\)
\(\Rightarrow\left(2016+\frac{1}{2016}\right)\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2016+\frac{1}{1016}=0\text{ (loại vì }2016+\frac{1}{2016}>0\text{)}\text{ }\\x-1=0\end{cases}}\)
\(\Rightarrow x=1\)
\(2016x+x\frac{1}{2016}-2016=\frac{1}{2016}\)
\(\Leftrightarrow x\left(2016+\frac{1}{2016}\right)=\frac{1}{2016}+2016\)
\(\Leftrightarrow x=\left(2016+\frac{1}{2016}\right):\left(2016+\frac{1}{2016}\right)\)
\(\Leftrightarrow x=1\)
\(2016x+x\frac{1}{2016}-2016=\frac{1}{2016}\)
=> \(2016x+\frac{2016x+1}{2016}-2016=\frac{1}{2016}\)
=> \(2016x+x+\frac{1}{2016}-2016=\frac{1}{2016}\)
=> \(2017x-2016=\frac{1}{2016}-\frac{1}{2016}\)
=> \(2017x-2016=0\)
=> \(2017x=2016\)
=> \(x=2016:2017\)
=> \(x=\frac{2016}{2017}\)
