\(\Leftrightarrow\dfrac{x}{2005}+1+\dfrac{x-1}{2006}+1=\dfrac{x-2}{2007}+1-1+1\)
\(\Leftrightarrow\dfrac{x+2005}{2005}+\dfrac{x+2005}{2006}=\dfrac{x+2005}{2007}\)
\(\Leftrightarrow\left(x+2005\right)\left(\dfrac{1}{2005}+\dfrac{1}{2006}-\dfrac{1}{2007}\right)=0\)
\(\Leftrightarrow x+2005=0\) (vì \(\dfrac{1}{2005}+\dfrac{1}{2006}-\dfrac{1}{2007}\ne0\))
\(\Leftrightarrow x=-2005\)
\(\dfrac{x}{2005}+\dfrac{x-1}{2006}=\dfrac{x-2}{2007}-1\)
\(\Leftrightarrow\dfrac{x+2005}{2005}+\dfrac{x+2005}{2006}-\dfrac{x+2005}{2007}=0\)
\(\Leftrightarrow\left(x+2005\right)\left(\dfrac{1}{2005}+\dfrac{1}{2006}-\dfrac{1}{2007}\right)=0\)
\(\Leftrightarrow x=-2005\).
\(\dfrac{x}{2005}+\dfrac{x-1}{2006}=\dfrac{x-2}{2007}-1\\ \dfrac{x}{2005}+1+\dfrac{x-1}{2006}+1=\dfrac{x-2}{2007}+1\\ \dfrac{x+2005}{2005}+\dfrac{x+2005}{2006}=\dfrac{x+2005}{2007}\\ \left(x+2005\right)\left(\dfrac{1}{2005}+\dfrac{1}{2006}-\dfrac{1}{2007}\right)=0\\ =>x+2005=0\\ =>x=-2005\)
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