Question on solving an equation with "max" functions

edit

I tried the following command

var('p,v,a,f,m,d,g,n,e')
(p==v/(a+max_symbolic(f/(m/a),f/(p*d))+max_symbolic(g/(n/a),g/(p*e)))).solve(p)

to try to get a closed form for p, but the function that came back contained p:

[p == v/(a + max(a*f/m, f/(d*p)) + max(a*g/n, g/(e*p)))]

I am a complete ignoramus using SAGE but I've had luck before simplifying similar equations to get a closed form. Any ideas?

Thanks