\(\frac{x+1}{2009}+\frac{x+3}{2007}=\frac{x+5}{2005}+\frac{x+17}{1993}\\ \Leftrightarrow\frac{x+1}{2009}+1+\frac{x+3}{2007}+1=\frac{x+5}{2005}+1+\frac{x+17}{1993}\\ \Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2007}-\frac{x+2010}{2005}-\frac{x+2010}{1993}=0\\ \Leftrightarrow\left(x+2010\right)\left(\frac{1}{2009}+\frac{1}{2007}-\frac{1}{2005}-\frac{1}{1993}\right)=0\\ \Leftrightarrow x+2010=0\\ \Leftrightarrow x=-2010\)
Vậy tập nghiệm của phương trình trên là \(S=\left\{-2010\right\}\)
\(\frac{x+1}{2009}+\frac{x+3}{2007}=\frac{x+5}{2005}+\frac{x+7}{1993}\Leftrightarrow\frac{x+1}{2009}+1+\frac{x+3}{2007}+1=\frac{x+5}{2005}+1+\frac{x+7}{1993}+1\)
\(\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2007}=\frac{x+2010}{2005}+\frac{x+2010}{1993}\Leftrightarrow\frac{x+2010}{2009}+\frac{x+2010}{2007}-\frac{x+2010}{2005}-\frac{x+2010}{1993}=0\)
\(\Leftrightarrow\left(x-2010\right)\left(\frac{1}{2009}+\frac{1}{2007}-\frac{1}{2005}-\frac{1}{1993}\right)=0\)
\(\Leftrightarrow x-2010=0\Leftrightarrow x=2010\)
Vậy \(x=2010\)
