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[tex]\frac{x+1}{2009}+\frac{x+2}{2008}+\frac{x+3}{2007}=\frac{x+4}{2006}+\frac{x+5}{2005}+\frac{x+6}{2004}\Leftrightarrow \frac{x+1}{2009}+1+\frac{x+2}{2008}+1+\frac{x+3}{2007}+1=\frac{x+4}{2006}+1+\frac{x+5}{2005}+1+\frac{x+6}{2004}+1\Leftrightarrow \frac{x+2010}{2009}+\frac{x+2010}{2008}+\frac{x+2010}{2007}=\frac{x+2010}{2006}+\frac{x+2010}{2005}+\frac{x+2010}{2004}\Leftrightarrow (x+2010)(\frac{1}{2009}+\frac{1}{2008}+\frac{1}{2007}-\frac{1}{2006}-\frac{1}{2005}-\frac{1}{2004})=0\Leftrightarrow x=-2010[/tex]
 
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