Simplifying the Boolean expression $A + \bar{A}\bar{B}$?

Question

So I'm trying to simplify the Boolean expression (1) $A + \bar{A}\bar{B}$.

I noticed that by Karnaugh maps this is equivalent to $A+\bar{B}$, and I also noticed that if I take the complement of (1), I get ~(1)= $\bar{A}(A + B) = \bar{A}A + \bar{A}B = \bar{A}B$, so then taking complements again yields (1) = $A + \bar{B}$.

But this feels very ad hoc to me, and makes me feel like I'm missing some key point about how to simplify this expression more systematically.

Any thoughts appreciated.

Thanks.