Need the help of a Fibonacci + phi expert

[Thomas Baruchel]

Hi,

I know some of you are real expert in transforming expressions containing
Fibonacci / Lucas / phi numbers.
I already managed to find the following closed forms, but I am sure it is
possible to find more compact.
I like rather a phi-based form (easier to handle through analytic methods),
but if someong finds something really amazing by using F or L, why not ?

I am looking better for the 4 following forms :

a) The two forms :
1/(2phi) + phi^2 sqrt( (9 phi^(4n) - 3 phi^(2n)-1) / (phi^(4n+6) + 
phi^(2n+3) - 1))/2
(phi^(2n+3) + phi + phi sqrt(9 phi^(4n+4)-22 phi^(2n+2) + 9))/(2 
phi^(2n+4)-2)

b) the homographic transformation of the two previous forms with
f(x) = ( F(n) + x F(n+1) )/ ( F(n+1) + x F(n+2) )
where F is the Fibonacci sequence with offset 0 :
F(0) = 0
F(1) = 1
F(2) = 1
F(3) = 2
etc.