Ta có: \(\frac{x-1}{2013}+\frac{x-2}{2012}=\frac{x-3}{2011}+\frac{x-4}{2010}\)
\(\Rightarrow\frac{x-1}{2013}+1+\frac{x-2}{2012}+1=\frac{x-3}{2011}+1+\frac{x-4}{2010}+1\)
\(\Rightarrow\frac{x-2014}{2013}+\frac{x-2014}{2012}+\frac{x-2014}{2011}+\frac{x-2014}{2010}=0\)
\(\Rightarrow\left(x-2014\right).\left(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2011}\right)=0\)
Vì \(\frac{1}{2013}+\frac{1}{2012}+\frac{1}{2011}+\frac{1}{2010}\ne0\)
=> x - 2014 =0
=> x = 2014
Vậy x = 2014
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