\frac{x-p}{2008-p} = \frac{x-(2008-p)}{p} \Rightarrow x\cdot p - p^2 = x(2008-p)-(2008-p)^2\Rightarrow x(2008-2p)=(2008-p)^2-p^2\Rightarrow x(2008-2p)=(2008-2p)\cdot 2008\Rightarrow x=2008