Giải các phương trình sau : x/2000+(x+1)/2001+(x+2)/2002+(x+3)/2004=5

* Hướng dẫn giải

$\begin{array}{l}\frac{x}{2000}+\frac{x+1}{2001}+\frac{x+2}{2002}+\frac{x+3}{2003}+\frac{x+4}{2004}=5\\ \iff \left(\frac{x}{2000}-1\right)+\left(\frac{x+1}{2001}-1\right)+\left(\frac{x+2}{2002}-1\right)+\left(\frac{x+3}{2003}-1\right)+\left(\frac{x+4}{2004}-1\right)=0\\ \iff \frac{x-2000}{2000}+\frac{x-2000}{2001}+\frac{x-2000}{2002}+\frac{x-2000}{2003}+\frac{x-2000}{2004}=0\\ \iff \left(x-2000\right)\left(\frac{1}{2000}+\frac{1}{2001}+\frac{1}{2002}+\frac{1}{2003}+\frac{1}{2004}\right)=0\iff x=2000\end{array}$