Ta có :
$\dfrac{x+2}{2013} + \dfrac{x+3}{2012} = \dfrac{x+4}{2011} + \dfrac{x+5}{2010} $
$ ⇔ (\dfrac{x+2}{2013}+1) + (\dfrac{x+3}{2012} +1)= (\dfrac{x+4}{2011}+1) + (\dfrac{x+5}{2010} +1)$
$⇔ \dfrac{x+2015}{2013} + \dfrac{x+2015}{2012} = \dfrac{x+2015}{2011} + \dfrac{x+2015}{2010}$
$⇔(x+2015).(\dfrac{1}{2013} + \dfrac{1}{2012} -\dfrac{1}{2011} + \dfrac{1}{2010} ) = 0$
$⇔x+2015=0$
$⇔x=-2015$