$\text{Đáp án + Giải thích các bước giải:}$
`(x-2)/(2019)+(x-9)/(2012)+(x)/(2021)=(x+1)/(674)`
`<=>((x-2)/(2019)-1)+((x-9)/(2012)-1)+((x)/(2021)-1)=(x+1)/(674)-3`
`<=>((x-2)/(2019)-(2019)/(2019))+((x-9)/(2012)-(2012)/(2012))+((x)/(2021)-(2021)/(2021))=(x+1)/(674)-(2022)/(674)`
`<=>(x-2-2019)/(2019)+(x-9-2012)/(2012)+(x-2021)/(2021)=(x+1-2022)/(674)`
`<=>(x-2021)/(2019)+(x-2021)/(2012)+(x-2021)/(2021)-(x-2021)/(674)=0`
`<=>(x-2021)((1)/(2019)+(1)/(2012)+(1)/(2021)-(1)/(674))=0`
`<=>x-2021=0` `\text{. Do}` ` (1)/(2019)+(1)/(2012)+(1)/(2021)-(1)/(674)\ne0`
`<=>x=2021`
`\text{Vậy}` `S={2021}`
