=>\left ( \frac{x+4}{2000}+1 \right ) + \left ( \frac{x+3}{2001}+ 1 \right ) = \left ( \frac{x+2}{2002} +1\right ) + \left ( \frac{x+1}{2003}+ 1 \right )=>\left ( \frac{x+4+ 2000}{2000} \right ) + \left ( \frac{x+3+2001}{2001} \right ) - $\left ( \frac{x+2+2002}{20002} \right )$ + \left ( \frac{x+1+2003}{2003} \right ) = 0 =>\left ( \frac{x+2004}{2000} \right )+\left ( \frac{x+2004}{2001} \right ) - \left ( \frac{x+2004}{2002} \right ) + \left ( \frac{x+2004}{2003} \right ) = 0=>\left ( x+2004 \right ) $\left ( \frac{1}{2000} +\frac{1}{2001} +\frac{1}{2002} +\frac{1}{2003}\right ) =0=>Vì \left ( \frac{1}{2000} +\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}\right ) >0$=>$x$+$2004$ = $0$ => $x= -2004$
=>
\left ( \frac{x+4}{2000}+1 \right ) +
\left ( \frac{x+3}{2001}+ 1 \right ) =
\left ( \frac{x+2}{2002} +1\right ) +
\left ( \frac{x+1}{2003}+ 1 \right )=>
\left ( \frac{x+4+ 2000}{2000} \right ) +
\left ( \frac{x+3+2001}{2001} \right ) -
\left ( \frac{x+2+2002}{2002} \right ) - \left ( \frac{x+1+2003}{2003} \right ) =
0 =>
\left ( \frac{x+2004}{2000} \right )+
\left ( \frac{x+2004}{2001} \right ) -
\left ( \frac{x+2004}{2002} \right ) - \left ( \frac{x+2004}{2003} \right ) = 0
=>
\left ( x+2004 \right ) $\left ( \frac{1}{2000} +\frac{1}{2001}
-\frac{1}{2002}
-\frac{1}{2003}\right )
=0=>Vì \left ( \frac{1}{2000} +\frac{1}{2001}
-\frac{1}{2002}
-\frac{1}{2003}\right )
>
0$=>$x$+$2004$ = $0$ => $x=
-2004$