\(\Leftrightarrow\frac{x-1}{2011}+1+\frac{x-2}{2012}+1+\frac{x-3}{2013}+1+\frac{x-4}{2014}+1-\left(x+2010\right)=0\)
\(\Leftrightarrow\frac{x+2010}{2011}+\frac{x+2010}{2012}+\frac{x+2010}{2013}+\frac{x+2010}{2014}-\left(x+2010\right)=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}-1\right)=0\)
\(\Leftrightarrow x=-2010\)
\(\frac{x-1}{2011}+\frac{x-2}{2012}+\frac{x-3}{2013}+\frac{x-4}{2014}=x+2006\)
\(\Leftrightarrow\frac{x+2010}{2011}+\frac{x+2010}{2012}+\frac{x+2010}{2013}+\frac{x+2010}{2014}=x+2010\)
\(\Leftrightarrow\left(x+2010\right)\left(\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}\right)=x+2010\)
\(\Leftrightarrow\frac{1}{2011}+\frac{1}{2012}+\frac{1}{2013}+\frac{1}{2014}=1\left(\text{Vô lí}\right)\)
\(\text{Vậy phương trình vô nghiệm.}\)