\(\Leftrightarrow\left(\dfrac{x-1}{2004}+1\right)+\left(\dfrac{x-2}{2003}+1\right)-\left(\dfrac{x-3}{2002}+1\right)=\left(\dfrac{x-4}{2001}+1\right)\\\Leftrightarrow\dfrac{x-2005}{2004}+\dfrac{x-2005}{2003}-\dfrac{x-2005}{2002}-\dfrac{x-2005}{2001}=0\\ \Leftrightarrow\left(x-2005\right)\left(\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\right)=0\\ \Leftrightarrow x-2005=0\\ \Leftrightarrow x=2005\)
\(\dfrac{x-1}{2004}+\dfrac{x-2}{2003}-\dfrac{x-3}{2002}=\dfrac{x-4}{2001}\\ \Leftrightarrow\left(\dfrac{x-1}{2004}-1\right)+\left(\dfrac{x-2}{2003}-1\right)-\left(\dfrac{x-3}{2002}-1\right)=\dfrac{x-4}{2001}-1\\ \Leftrightarrow\dfrac{x-2005}{2004}+\dfrac{x-2005}{2003}-\dfrac{x-2005}{2002}-\dfrac{x-2005}{2001}=0\\ \Leftrightarrow\left(x-2005\right)\left(\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\right)=0\\ \Leftrightarrow x-2005=0\left(vì\dfrac{1}{2004}+\dfrac{1}{2003}-\dfrac{1}{2002}-\dfrac{1}{2001}\ne0\right)\\ \Leftrightarrow x=2005\)
