I assume that A.B is the conjunction ("and") of A and B. I'll skip the period below and will write ~A for not(A).

~A + AB can be simplified to ~A + B as follows:

~A + AB = ~A(1 + B) + AB = ~A + ~AB + AB = ~A + (~A + A)B = ~A + 1B = ~A + B.

To come up with this, I drew a Venn diagram of ~A + AB to see that it is ~A + B, then double-checked it using truth tables (without writing everything), and finally decided to represent B in the right-hand side, ~A + B, as (~A + A)B because the left-hand side, ~A + AB, contains AB.