Find all solutions where x and y are integers:

$\displaystyle \frac{1}{x} + \frac{1}{y} = \frac{1}{14}$

this can be rearranged to:

$\displaystyle \frac{xy}{x + y} = 14$

I know how to solve diophantine equations of the form

$\displaystyle ax + by = c$

Obviously the given equation is in a different form. How do I solve?