Đáp án:
`x=-2012`
Giải thích các bước giải:
`\frac{x+4}{2008}+\frac{x+3}{2009}=\frac{x+2}{2010}+\frac{x+1}{2011}`
`⇒ \frac{x+4}{2008}+1+\frac{x+3}{2009}+1=\frac{x+2}{2010}+1+\frac{x+1}{2011}+1`
`⇒\frac{x+2012}{2008}+\frac{x+2012}{2009}=\frac{x+2012}{2010}+\frac{x+2012}{2011}`
`⇒\frac{x+2012}{2008}+\frac{x+2012}{2009}-\frac{x+2012}{2010}-\frac{x+2012}{2011}=0`
`⇒(x+2012)(\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011})=0`
Do `\frac{1}{2008}+\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011} \ne 0`
`⇔x+2012=0`
`⇒x=-2012`
