Đáp án:
`text{x = -2011}`
Giải thích các bước giải:
`(x+1)/2010 + (x+2)/2009 = (x+3)/2008 + (x+4)/2007`
`to ( (x+1)/2010 + 1 ) + ( (x+2)/2009 + 1 ) = ( (x+3)/2008 + 1 ) + ( (x+4)/2007 + 1 )`
`to (x+2011)/2010 + (x+2011)/2009 = (x+2011)/2008 + (x+2011)/2007`
`to (x+2011)/2010 + (x+2011)/2009 - (x+2011)/2008 - (x+2011)/2007 = 0 `
`to (x+2011) . ( 1/2010 + 1/2009 - 1/2008 - 1/2007 ) = 0`
Mà `1/2010 + 1/2009 - 1/2008 - 1/2007 ne 0`
`to x+2011=0`
`to x = -2011`
`text{Vậy x = -2011}`