\(\frac{x+1}{2014}+\frac{x+2}{2013}+\frac{x+3}{2012}=\frac{3x+12}{2011}\)
\(\Leftrightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)+\left(\frac{x+3}{2012}+1\right)=\frac{3x+12}{2011}+3\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}=\frac{3x+6045}{2011}\)
\(\Leftrightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}+\frac{x+2015}{2012}-\frac{3\left(x+2015\right)}{2011}=0\)
\(\Leftrightarrow\left(x+2015\right)\left(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{3}{2011}\right)=0\)
Mà \(\frac{1}{2014}+\frac{1}{2013}+\frac{1}{2012}-\frac{3}{2011}\ne0\)
\(\Leftrightarrow x+2015=0\)
\(\Leftrightarrow x=-2015\)
Vậy x = -2015
