Math Is Fun Forum

You choose three POSITIVE integers: x, y and z.
The quotients                 1. (x*y)/(x+y)
                                    2. (x*z)/(x+z)
                                    3. (y*z)/(y+z)
shall also be integers.
So, then one has to prove the integers x, y and z have a factor in common which is bigger than 1.

The problem is that I absolutely don't know how to prove this.