Đáp án:
`S=\{-2009\}`
Giải thích các bước giải:
`\frac{x+1}{2008}+\frac{x}{2009}=\frac{x-1}{2010}+\frac{x-2}{2011}`
`⇔\frac{x+1}{2008}+1+\frac{x}{2009}+1=\frac{x-1}{2010}+1+\frac{x-2}{2011}+1`
`⇔\frac{x+1+2008}{2008}+\frac{x+2009}{2009}=\frac{x-1+2010}{2010}+\frac{x-2+2011}{2011}`
`⇔\frac{x+2009}{2008}+\frac{x+2009}{2009}=\frac{x+2009}{2010}+\frac{x+2009}{2011}`
`⇔\frac{x+2009}{2008}+\frac{x+2009}{2009}-\frac{x+2009}{2010}-\frac{x+2009}{2011}=0`
`⇔(x+2009)(1/2008+1/2009-1/2010-1/2011)=0`
`⇔x+2009=0` `(vì 1/2008+1/2009-1/2010-1/2011\ne 0)`
`⇔x=-2009`
Vậy `S=\{-2009\}`
