. Ta có: \(\frac{x+1}{2016}+\frac{x+3}{2014}=\frac{x+5}{2012}+\frac{x+7}{2010}\) \(\Leftrightarrow\frac{x+1}{2016}+1+\frac{x+3}{2014}+1=\frac{x+5}{2012}+1\frac{x+7}{2010}+1\)
. \(\Leftrightarrow\frac{x+2017}{2016}+\frac{x+2017}{2014}-\frac{x+2017}{2012}-\frac{x+2017}{2010}=0\) \(\Leftrightarrow\left(x+2017\right)\left(\frac{1}{2016}+\frac{1}{2014}-\frac{1}{2012}-\frac{1}{2010}\right)\)
\(\Leftrightarrow x+2017=0\) \(\Leftrightarrow x=-2017\)
\(\frac{x+1}{2016}+\frac{x+3}{2014}=\frac{x+5}{2012}+\frac{x+7}{2010}\)
\(\Rightarrow\left(\frac{x+1}{2016}+1\right)+\left(\frac{x+3}{2014}+1\right)=\left(\frac{x+5}{2012}+1\right)+\left(\frac{x+7}{2010}+1\right)\)
\(\Rightarrow\frac{x+2017}{2016}+\frac{x+2017}{2014}=\frac{x+2017}{2012}+\frac{x+2017}{2010}\)
\(\Rightarrow\frac{x+2017}{2016}+\frac{x+2017}{2014}-\frac{x+2017}{2012}-\frac{x+2017}{2010}=0\)
\(\Rightarrow\left(x+2017\right)\left(\frac{1}{2016}+\frac{1}{2014}-\frac{1}{2012}-\frac{1}{2010}\right)=0\)
\(\Rightarrow x+2017=0\)\(\left(Vì\frac{1}{2016}+\frac{1}{2014}-\frac{1}{2012}-\frac{1}{2010}\ne0\right)\)
\(\Rightarrow x=0-2017\)
\(\Rightarrow x=-2017\)
Vậy x=-2017
