GIải phương trình: $\frac{x-3}{2011}$+ $\frac{x-2}{2012}$= $\frac{x-2012}{2}$+ $\frac{x-2011}{3}$

    $\dfrac{x – 3}{2011} + \dfrac{x-2}{2012} = \dfrac{x – 2012}{2} + \dfrac{x-2011}{3}$

⇔$(\dfrac{x-3}{2011} – 1) +(\dfrac{x-2}{2012} – 1) = (\dfrac{x-2012}{2} – 1) + (\dfrac{x-2011}{3} – 1)$

⇔$\dfrac{x-2014}{2011} + \dfrac{x-2014}{2012} – \dfrac{x-2014}{2} – \dfrac{x-2014}{3} = 0$

⇔$(x – 2014)(\dfrac{1}{2011} + \dfrac{1}{2012} – \dfrac{1}{2} – \dfrac{1}{3}) = 0$

⇔$x – 2014 = 0$$\textrm{(Vì}$$ \dfrac{1}{2011} + \dfrac{1}{2012} – \dfrac{1}{2} – \dfrac{1}{3} \neq 0)$

⇔$x = 2014$