Giait phương trình: Một cách dễ hiểu nhất `(x-1001)/(1006) +(x-1003)/(1004)+(x-1005)/(1002)+(x-1007)/(1000)=4`

$\dfrac{x-1001}{1006}+\dfrac{x-1003}{1004}+\dfrac{x-1005}{1002}+\dfrac{x-1007}{1000}=4$

$⇔\bigg(\dfrac{x-1001}{1006}-1\bigg)+\bigg(\dfrac{x-1003}{1004}-1\bigg)+\bigg(\dfrac{x-1005}{1002}-1\bigg)+\bigg(\dfrac{x-1007}{1000}-1\bigg)=0$

$⇔\dfrac{x-2007}{1006}+\dfrac{x-2007}{1004}+\dfrac{x-2007}{1002}+\dfrac{x-2007}{1000}=0$

$⇔(x-2007)\bigg(\dfrac{1}{1006}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}\bigg)=0$

Do $\dfrac{1}{1006}+\dfrac{1}{1004}+\dfrac{1}{1002}+\dfrac{1}{1000}>0$

$⇔x-2007=0$ 

$⇔x=2007$

Vậy phương trình có nghiệm `S={2007}`