Maxima, operation between functions

[fluidistic]

Hi guys, I've used google and Maxima's manual but couldn't find what I'm looking for.
I have defined a function similar to

Z(beta):=beta+3;

, and another function

P(beta):=beta+7/Z;

and I am not able to "simplify" P(beta) as beta+7/(beta+3).
I've tried several commands but all failed. I even tried to define

P(beta):=beta+7/%o1;

,

P(beta,Z):=beta+7/Z;

,

P(beta,Z(beta)):=beta+7/Z(beta);

and

P(beta,Z):=beta+7/Z(beta);

; all failed.
Any idea on how I could reach my goal?

 

[fluidistic]

Problem solved guys! I found it by "luck"... Answer: evaluate the following cell:

P(beta);