<s>[INST] Find the rational solution of the equation Find the rational solution of the equation:
$\frac{2x - 1}{2016} + \frac{2x - 3}{2014} + \frac{2x - 5}{2012}+ ...+ \frac{2x - 2011}{6} +\frac{2x - 2013}{4} + \frac{2x - 2015}{2} =\\ \frac{2x - 2016}{1} + \frac{2x - 2014}{3} + \frac{2x - 2012}{5}+ ...+ \frac{2x - 6}{2011} + \frac{2x - 4}{2013} + \frac{2x - 2}{2015}$
The problem is from a competition for seven graders. I tried various algebraic manipulations for no avail. Any hint will be highly appreciated.
 [/INST] Alpha gives $x=\frac {2017}2$.  With that value all the fractions become $1$ so each side sums to $1008$
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