It makes sense, on left is the quantity of the impurity that is left in the zone after dx has solidified, (1-x), and it is equal to the increase, dC_{L}, in the concentration in the shortening zone (L-x). then the result is as it should be.

But let me ask a mathematical question:

Why don't i have dx on the right side also, on the side of (L-x)?

L-x is shortening with the amount dx also.