Formula for flux of electrons in 1D from carrier density profile

This content was taken from https://ecee.colorado.edu/~bart/book/contents.htm.
In that they derive the diffusion current expression from this particular carrier density profile.
Their derivation is as follows.(the explanation given is also theirs)
The flux at x = 0 due to carriers that originate at x = -l and move from left to right equals:
$$Phi_{n,leftto right} = displaystylefrac{1}{2}v_{th}n(x=-l)$$
here $v_{th}$ is the thermal velocity of electrons.
where the factor 1/2 is due to the fact that only half of the carriers move to the left while the other half moves to the right.
The flux at x = 0 due to carriers that originate at x = +l and move from right to left, equals:
$$Phi_{n,rightto left} = displaystylefrac{1}{2}v_{th}n(x=l)$$
The total flux of carriers moving from left to right at x = 0 therefore equals:
$$Phi_n = Phi_{n,leftto right} – Phi_{n,rightto left} = displaystylefrac{1}{2}v_{th}[n(x=-l)-n(x=l)]$$
Given that the mean free path is small we can write the difference in densities divided by the distance between x = -l and x = l as the derivative of the carrier density:
$$Phi_n = -lv_{th}frac{[n(x=-l)-n(x=l)]}{2l} = -lv_{th}frac{dn}{dx}$$
and from this they derive the diffusion current.
But I don’t understand how they came up with the equation for flux at the first place.