>>13431837f(a,b) * f(b,c) = f(a,c) which means
f(a,b) = f(a,c) / f(b,c).
The c's cancel each other out when on top and bottom, which is division, so
f(a,b) = f(a,c) / f(b,c) = g(a) / g(b)
Here's another thing
1: f(a,c) = f(a,b) * f(b,c)
2: f(c,c) = f(c,b) * f(b,c)
divide then cross multiply eq1 and eq2
3: f(a,b) * f(c,c) = f(a,c) * f(c,b)
from eq1
4: f(a,c) * f(c,b) = f(a,b)
from eq3 and eq4
5: f(c,c) = 1
combine 2 and 5
6: 1 = f(c,b) * f(b,c) = f(c,c)
