\(PT\Leftrightarrow\left(\dfrac{x-1}{2000}-1\right)+\left(\dfrac{x-2}{1999}-1\right)=\left(\dfrac{x-3}{1998}-1\right)+\left(\dfrac{x-4}{1997}-1\right)\\ \Leftrightarrow\dfrac{x-2001}{2000}+\dfrac{x-2001}{1999}=\dfrac{x-2001}{1998}+\dfrac{x-2001}{1997}\\ \Leftrightarrow\left(x-2001\right)\left(\dfrac{1}{2000}+\dfrac{1}{1999}-\dfrac{1}{1998}-\dfrac{1}{1997}\right)=0\\ \Leftrightarrow x=2001\left(\dfrac{1}{2000}+\dfrac{1}{1999}-\dfrac{1}{1998}-\dfrac{1}{1997}\ne0\right)\)
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