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, dCL, 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.