Đáp án: x=2012
Giải thích các bước giải:
$\eqalign{ & \frac{{x - 1}}{{2011}} + \frac{{x - 2}}{{2010}} + \frac{{x - 3}}{{2009}} = 3 \cr & \Leftrightarrow (\frac{{x - 1}}{{2011}} - 1) + (\frac{{x - 2}}{{2010}} - 1) + (\frac{{x - 3}}{{2009}} - 1) = 0 \cr & \Leftrightarrow \frac{{x - 2012}}{{2011}} + \frac{{x - 2012}}{{2010}} + \frac{{x - 2012}}{{2009}} = 0 \cr & \Leftrightarrow (x - 2012)(\frac{1}{{2011}} + \frac{1}{{2010}} + \frac{1}{{2009}}) = 0 \cr & \Leftrightarrow x - 2012 = 0(do\,\frac{1}{{2011}} + \frac{1}{{2010}} + \frac{1}{{2009}} \ne 0) \cr & \Leftrightarrow x = 2012 \cr} $
