Ta có:
x-1/2009 + x-2/2008 = x-3/2007 + x-4/2006
=> (x-1/2009 - 1)+(x-2/2008 - 1) = (x-3/2007 - 1) + (x-4/2006 -1 )
=> x-2010/2009 + x-2010/2008 = x-2010/2007 + x-2010/2006
=> x-2010/2009 + x-2010/2008 - (x-2010/2007 + x-2010/2006)=0
=> (x-2010)(1/2009+1/2008-1/2007-1/2006)=0
Vì (1/2009+1/2008-1/2007-1/2006) KHÁC 0
=>x-2010=0
=>x=2010
\(\frac{x-1}{2009}+1+\frac{x-2}{2008}+1=\frac{x-3}{2007}+1+\frac{x-4}{2006}+1\)
\(\frac{x+2010}{2009}+\frac{x+2010}{2008}=\frac{x+2010}{2007}+\frac{x+2010}{2006}\)
\(\frac{x+2010}{2009}+\frac{x+2010}{2008}-\frac{x+2010}{2007}-\frac{x+2010}{2006}=0\)
\(\left(x+2010\right).\left(\frac{1}{2009}+\frac{1}{2008}-\frac{1}{2007}-\frac{1}{2006}\right)=0\)
Vì \(\left(\frac{1}{2009}+\frac{1}{2008}-\frac{1}{2007}-\frac{1}{2006}\right)\ne0\)
\(\Rightarrow x+2010=0\)
\(\Rightarrow x=-2010\)