Giải phương trình (frac{{x + 1}}{{2013}} + frac{{x + 2}}{{2012}} = frac{{x + 3}}{{2011}} + frac{{x + 4}}{{2010}})

* Hướng dẫn giải

\(\begin{array}{l}
\left( {\frac{{x + 1}}{{2013}} + 1} \right) + \left( {\frac{{x + 2}}{{2012}} + 1} \right) = \left( {\frac{{x + 3}}{{2011}} + 1} \right) + \left( {\frac{{x + 4}}{{2010}} + 1} \right)\\
 \Leftrightarrow \frac{{\left( {x + 2014} \right)}}{{2013}} + \frac{{\left( {x + 2014} \right)}}{{2012}} - \frac{{\left( {x + 2014} \right)}}{{2011}} - \frac{{\left( {x + 2014} \right)}}{{2010}} = 0\\
 \Leftrightarrow (x + 2014)\left( {\frac{1}{{2013}} + \frac{1}{{2012}} - \frac{1}{{2011}} - \frac{1}{{2010}}} \right)
\end{array}\)

<=> (x + 2014) = 0  Vì \(\left( {\frac{1}{{2013}} + \frac{1}{{2012}} - \frac{1}{{2011}} - \frac{1}{{2010}}} \right) \ne 0\)

<=> x = -2014