How do you get from Fnet=ρf-ρo to Fg/Fb=ρo/ρf?

[mummy]

This has to do with buoyancy.
You can substitute Fnet for Fg-Fb.
ρ is not the letter p it is the symbol for density.
ρo = density of an object
ρf = density of the fluid
Fg = force of gravity
Fb = buoyant force

[markum]

Fnet = Fb - Fg since Fnet is the net force

Plugging into the first equation above, with object volume V and gravity g:

Fb - Fg = (pf - p0) * V * g

Dividing both sides by Fg = p0 * V * g

(Fb - Fg) / Fg = (pf - p0) * V * g / Fg
(Fb - Fg) / Fg = (pf - p0) * V * g / (p0 * V * g)
Fb/Fg - 1 = pf / p0 - 1
Fb/Fg = pf / p0

Done, although both sides need to be flipped