Hi everybody! Problem: I don't know how to find an explicit form for this sum, anyone can help me?

$\displaystyle \sum_{k=-\infty}^{+\infty}\frac{1}{|x-kx_0|}$

here the calculations I made, but don't bring me anywhere:

https://dl.dropbox.com/u/8281720/SAM_1625.JPG

and my prof's version (I'm not sure he could be so quick on the absolute value)

https://dl.dropbox.com/u/8281720/photo.JPG

Thanks!