$\text{Đáp án + Giải thích các bước giải:}$
`(x+3)/(2012)+(x+2)/(2013)=(x+2012)/(3)+(x+2011)/(4)`
`<=>((x+3)/(2012)+1)+((x+2)/(2013)+1)=((x+2012)/(3)+1)+((x+2011)/(4)+1)`
`<=>(x+3+2012)/(2012)+(x+2+2013)/(2013)=(x+2012+3)/(3)+(x+2011+4)/(4)`
`<=>(x+2015)/(2012)+(x+2015)/(2013)-(x+2015)/(3)-(x+2015)/(4)=0`
`<=>(x+2015)((1)/(2012)+(1)/(2013)-(1)/(3)-(1)/(4))=0`
`<=>x+2015=0` `\text{. Do}` `(1)/(2012)+(1)/(2013)-(1)/(3)-(1)/(4)\ne0`
`<=>x=-2015`
`\text{Vậy}` `S={-2015}`