giải phương trình sau : x-13/501+x-17/2000=x-15/1001+x-16/667

$\frac{x-13}{501}+$ $\frac{x-17}{2000}=$ $\frac{x-15}{1001}+$ $\frac{x-16}{667}$

$⇔(\frac{x-13}{501}-4)+($ $\frac{x-17}{2000}-1)-($ $\frac{x-15}{1001}-2)-($ $\frac{x-16}{667}-3)=0$

$⇔\frac{x-2017}{501}+$ $\frac{x-2017}{2000}-$ $\frac{x-2017}{1001}-$ $\frac{x-2017}{667}=0$

$⇔(x-2017)(\frac{1}{501}+$ $\frac{1}{2000}-$ $\frac{1}{1001}-$ $\frac{1}{667})=0$

$⇔x-2017=0$ (Vì:$\frac{1}{501}+$ $\frac{1}{2000}-$ $\frac{1}{1001}-$ $\frac{1}{667})$$\neq$ 0)

⇔x=2017

Vậy S={2017}