\(\frac{x+3}{2007}-\frac{x+3}{2008}=\frac{x+3}{2010}-\frac{x+3}{2009}\)
\(\Leftrightarrow\)\(\frac{x+3}{2007}-\frac{x+3}{2008}-\frac{x+3}{2010}+\frac{x+3}{2009}=0\)
\(\Leftrightarrow\) \(\left(x+3\right).\left(\frac{1}{2007}+\frac{1}{2008}-\frac{1}{2010}+\frac{1}{2009}\right)=0\)
\(\Leftrightarrow\) \(x+3=0\) ( Vì \(\frac{1}{2007}+\frac{1}{2008}-\frac{1}{2010}+\frac{1}{2009}\ne0\) )
\(\Leftrightarrow\) \(x=-3\)
Vậy x = -3
\(\frac{x+3}{2007}-\frac{x+3}{2008}=\frac{x+3}{2010}-\frac{x+3}{2009}\)
\(\Rightarrow\frac{x+3}{2007}-\frac{x+3}{2008}-\frac{x+3}{2010}+\frac{x+3}{2009}=0\)
\(\Rightarrow\left(x+3\right)\left(\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2010}+\frac{1}{2009}\right)=0\)
\(\Rightarrow x+3=0\Leftrightarrow x=-3\)
\(\frac{x+3}{2007}-\frac{x+3}{2008}=\frac{x+3}{2010}-\frac{x+3}{2009}\)
\(\Rightarrow\frac{x+3}{2007}-\frac{x+3}{2008}-\frac{x+3}{2010}+\frac{x+3}{2009}=0\)
\(\Rightarrow\left(x+3\right)\left(\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2010}+\frac{1}{2009}\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x+3=0\\\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2010}+\frac{1}{2009}\ne0\end{cases}\hept{\begin{cases}x=-3\\\frac{1}{2007}-\frac{1}{2008}-\frac{1}{2010}+\frac{1}{2009}\ne0\end{cases}}}\)
\(\Rightarrow x=-3\)
