Đáp án: $x=2009$
Giải thích các bước giải:
Ta có:
$\dfrac{2-x}{2007}-1=\dfrac{1-x}{2008}-\dfrac{x}{2009}$
$\to \dfrac{2-x}{2007}+1=\dfrac{1-x}{2008}-\dfrac{x}{2009}+2$
$\to \dfrac{2-x}{2007}+1=(\dfrac{1-x}{2008}+1)+(1-\dfrac{x}{2009})$
$\to \dfrac{2-x+2007}{2007}=\dfrac{1-x+2008}{2008}+\dfrac{2009-x}{2009}$
$\to \dfrac{2009-x}{2007}=\dfrac{2009-x}{2008}+\dfrac{2009-x}{2009}$
$\to \dfrac{2009-x}{2008}+\dfrac{2009-x}{2009}-\dfrac{2009-x}{2007}=0$
$\to (2009-x)(\dfrac{1}{2008}+\dfrac{1}{2009}-\dfrac{1}{2007})=0$
$\to 2009-x=0$
$\to x=2009$
