Find the rational solution of the equation

Question

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.

Answer 1

Alpha gives $x=\frac {2017}2$. With that value all the fractions become $1$ so each side sums to $1008$

Answer 2

Every term is $\dfrac{2x-2k}{2015-2k+2}-\dfrac{2x-(2k-1)}{2016-2k+2}=\dfrac{2x-2017}{(2016-2k+2)(2015-2k+2)}$