Tìm x biết: x-1/2011 x-2/2010-x-3/2009=x-4/2008

Lời giải:

\(\frac{{x - 1}}{{2011}} + \frac{{x - 2}}{{2010}} - \frac{{x - 3}}{{2009}} = \frac{{x - 4}}{{2008}}\)

\(\frac{{x - 1}}{{2011}} + \frac{{x - 2}}{{2010}} = \frac{{x - 3}}{{2009}} + \frac{{x - 4}}{{2008}}\)

\(\left( {\frac{{x - 1}}{{2011}} - 1} \right) + \left( {\frac{{x - 2}}{{2010}} - 1} \right) = \left( {\frac{{x - 4}}{{2008}} - 1} \right) + \left( {\frac{{x - 3}}{{2009}} - 1} \right)\)

\(\frac{{x - 2012}}{{2011}} + \frac{{x - 2012}}{{2010}} = \frac{{x - 2012}}{{2009}} + \frac{{x - 2012}}{{2008}}\)

\(\left( {x - 2012} \right)\left( {\frac{1}{{2011}} + \frac{1}{{2010}} - \frac{1}{{2009}} - \frac{1}{{2008}}} \right) = 0\)

Vì \(\frac{1}{{2011}} + \frac{1}{{2010}} - \frac{1}{{2009}} - \frac{1}{{2008}} \ne 0\)

Suy ra: x – 2012 = 0

Hay x = 2012

Vậy x = 2012