\(\frac{x+1}{2014}+\frac{x+2}{2013}=\frac{x+3}{2012}+\frac{x+4}{2011}\)
\(\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)=\left(\frac{x+3}{2012}+1\right)+\left(\frac{x+4}{2011}+1\right)\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}=\frac{x+2015}{2012}+\frac{x+2015}{2011}\)
\(\frac{x+2015}{2014}+\frac{x+2015}{2013}-\frac{x+2015}{2012}-\frac{x+2015}{2011}=0\)
\(\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\right)=0\)
\(\Rightarrow\hept{\begin{cases}x+2015=0\\\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}=0\end{cases}}\)
Vì \(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\ne0\Rightarrow x+2015=0\Rightarrow x=-2015\)
Vậy x = 2015 nha bn
\(\frac{x+1}{2014}+\frac{x+2}{2013}=\frac{x+3}{2012}+\frac{x+4}{2011}\)
\(\Rightarrow\left(\frac{x+1}{2014}+1\right)+\left(\frac{x+2}{2013}+1\right)=\left(\frac{x+3}{2012}+1\right)+\left(\frac{x+4}{2011}+1\right)\)
\(\Rightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}=\frac{x+2015}{2012}+\frac{x+2015}{x+2011}\)
\(\Rightarrow\frac{x+2015}{2014}+\frac{x+2015}{2013}-\frac{x+2015}{2012}-\frac{x+2015}{2011}=0\)
\(\Rightarrow\left(x+2015\right).\left(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\right)\)
Vì \(\frac{1}{2014}+\frac{1}{2013}-\frac{1}{2012}-\frac{1}{2011}\ne0\Rightarrow\left(x-2015\right)=0\)
\(\Rightarrow x=0+2015\) =2015
Đúng thì k ủng hộ mik nha mn!
