Proving time dilation formula for GPS satellites

[Wingeer]

Homework Statement

I recently had a test in the theory of relativity, and there was one task which I could not solve. This one has bothered me since the day I had the test.
It was a compound task about GPS-satellites.
There is no tricky calculations, or anything like that. The task aims at proving an expression.

$$\frac{{t_e }}{{\sqrt {1 - \frac{{2\gamma M}}{{c^2 r}}} }} = \frac{{t_s }}{{\sqrt{1 - \frac{{2\gamma M}}{{c^2 (r + h)}}} }}\$$

Where $${t_e }\$$ is the time on Earth's surface, $${t_s }\$$ is the time for the satellite, r is the radius from the center of Earth to the surface.

Homework Equations

$$\tau = \sqrt {1 - \frac{{2\gamma M}}{{c^2 r}}} t\$$

The Attempt at a Solution

I've tried a lot of editing these expressions, but it didn't get me anywhere. I really do not now how to prove the expression. I do imagine that there are some theory I need to figure, so that I can do something quirky with the expressions or something.

 

[Wingeer]

Oh. It looks like something happened to the LaTex-codes. Any ideas of what to do?