\(\frac{x+4}{2008}+\frac{x+3}{2009}=\frac{x+2}{2010}+\frac{x+1}{2011}\)
=> \(\left(\frac{x+4}{2008}+1\right)+\left(\frac{x+3}{2009}+1\right)=\left(\frac{x+2}{2010}+1\right)+\left(\frac{x+1}{2011}+1\right)\)
=> \(\frac{x+4+2008}{2008}+\frac{x+3+2009}{2009}=\frac{x+2+2010}{2010}+\frac{x+1+2011}{2011}\)
=> \(\frac{x+2012}{2008}+\frac{x+2012}{2009}=\frac{x+2012}{2010}+\frac{x+2012}{2011}\)
=> \(\frac{x+2012}{2008}+\frac{x+2012}{2009}-\frac{x+2012}{2010}-\frac{x+2012}{2011}=0\)
=> \(\left(x+2012\right)\left(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)
Do \(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\ne0\)
=> x + 2012 = 0 => x = -2012
x+1/2008 + x+3/2009 = x+2/2010 + x+1/2011
suy ra : x+2012/2008 + x+2012/2009 = x+2012/2010 + x+2012/2011
Tương đương : (x+2012) . (1/2008 + 1/2009 = 1/2010 - 1/2011)=0
Tương đương : x+2012 = 0
suy ra : 0 - 2012
= -2012
Vậy x = -2012
\(\frac{x+4}{2008}+\frac{x+3}{2009}=\frac{x+2}{2010}+\frac{x+1}{2011}\)
\(\Rightarrow\frac{x+4}{2008}+1+\frac{x+3}{2009}+1=\frac{x+2}{2010}+1+\frac{x+1}{2011}+1\)
\(\Rightarrow\frac{x+2012}{2008}+\frac{x+2012}{2009}=\frac{x+2012}{2010}+\frac{x+2012}{2011}\)
\(\Rightarrow\left(x+2012\right)\left(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)
mà \(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\ne0\)
nên \(x+2012=0\Rightarrow x=-2012\)
\(\frac{x+4}{2008}+\frac{x+3}{2009}=\frac{x+2}{2010}+\frac{x+1}{2011}\)
\(\Rightarrow\left(\frac{x+4}{2008}+1\right)+\left(\frac{x+3}{2009}+1\right)=\left(\frac{x+2}{2010}+1\right)+\left(\frac{x+1}{2011}+1\right)\)
\(\Rightarrow\frac{x+4+2008}{2008}+\frac{x+3+2009}{2009}=\frac{x+2+2010}{2010}+\frac{x+1+2011}{2011}\)
\(\Rightarrow\frac{x+2012}{2008}+\frac{x+2012}{2009}=\frac{x+2012}{2010}+\frac{x+2012}{2011}\)
\(\Rightarrow\frac{x+2012}{2008}+\frac{x+2012}{2009}-\frac{x+2012}{2010}-\frac{x+2012}{2011}=0\)
\(\Rightarrow\left(x+2012\right)\left(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)
Do \(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\ne0\)
\(\Rightarrow x+2012=0\Rightarrow x=-2012\)
