\(\dfrac{x+1}{2009}+\dfrac{x+3}{2007}=\dfrac{x+5}{2005}+\dfrac{x+7}{1993}\)
\(\Leftrightarrow\dfrac{x+1}{2009}+1+\dfrac{x+3}{2007}+1=\dfrac{x+5}{2005}+1+\dfrac{x+7}{1993}+1\)
\(\Leftrightarrow\dfrac{x+1+2009}{2009}+\dfrac{x+3+2007}{2007}=\dfrac{x+5+2005}{2005}+\dfrac{x+7+1993}{1993}\)
\(\Leftrightarrow\dfrac{x+2010}{2009}+\dfrac{x+2010}{2007}=\dfrac{x+2010}{2005}+\dfrac{x+2000}{1993}\)
\(\Leftrightarrow\dfrac{x+2010}{2009}+\dfrac{x+2010}{2007}-\dfrac{x+2010}{2005}-\dfrac{x+2000}{1993}=0\)
\(\Leftrightarrow\left(x+2010\right)\left(\dfrac{1}{2009}+\dfrac{1}{2007}-\dfrac{1}{2005}-\dfrac{1}{1993}\right)=-\dfrac{10}{1993}\)
\(\Leftrightarrow x+2010=-\dfrac{10}{1993}:\left(\dfrac{1}{2009}+\dfrac{2}{2007}-\dfrac{1}{2005}-\dfrac{1}{1993}\right)\)
\(\Leftrightarrow x=-\dfrac{10}{1993}:\left(\dfrac{1}{2009}+\dfrac{2}{2007}-\dfrac{1}{2005}-\dfrac{1}{1993}\right)-2010\)
( Chịu gòi :v )
\(\Leftrightarrow\dfrac{x+1}{2009}+1+\dfrac{x+3}{2007}+1=\dfrac{x+5}{2005}+1+\dfrac{x+7}{2003}+1\)
=>x+2010=0
hay x=-2010
