I see no such maths, anywhere in your post.

Here is some simple math, of course I realize it will not make a difference with you since you are just trolling, but it seemed sort of fun to play with some numbers...

Looking at the example of the Andromeda galaxy and the Milky way galaxy.

Distance between the 2 galaxies - 2,537,000 ly = 0.78 Mpc

The closing speed of the 2 galaxies is 400,000 km/hr

Hubble constant - 260,000 km/hr/Mpc

Expansion rate of space between Andromeda and the Milky way: $$0.78 Mpc \times 260,000 km/hr/Mpc = 203,000 km/hr$$

So the relative movement

__through space__ of the 2 galaxies

__if there was no expansion__ would be 600,000 km/hr

At what distance is the closing speed through space equal to the expansion of space:

$$\frac{600,000 km/hr}{ 260,000 km/hr/Mpc} = 2.3 Mpc$$

So simply looking at the current closing speed of the Andromeda galaxy, if the galaxy was 'magically' moved to > 2.3 Mpc from the Milky way galaxy, then they would be receding from each other. The actual velocity through space of the galaxy would be less than the expansion of space between the galaxies.

Hopefully I did not make any conceptual or math errors.