⇔$(\frac{x+1}{2004}+1)+$ $(\frac{x+2}{2003}+1)-($ $\frac{x+3}{2002}+1)-$ $(\frac{x+4}{2001}+1)=0$
<=>$\frac{x+2005}{2004}+$ $\frac{x+2005}{2003}-$ $\frac{x+2005}{2002}-$$\frac{x+2005}{2001}=0$
<=>$(x+2005)($$\frac{1}{2004}+$ $\frac{1}{2003}-$ $\frac{1}{2002}-$ $\frac{1}{2001)=0}$
⇔x+2005=0 (Vì:$\frac{1}{2004}+$ $\frac{1}{2003}-$ $\frac{1}{2002}-$ $\frac{1}{2001)}$ ∦0
⇔x=-2005