Prove A + ĀB = A +B using theorems and laws of Boolean Algebra?

Question

Fresh and invigorated after completing her algebra homework, Mimi appeared at the living room door.
She held a piece of paper covered in scribbled numbers, 'm's, 'd's and equations.
"Dad!" She announced.
"Five years from now you'll be only double my age!"
"Amazing!" Dad almost looked up from the TV, but knew she hadn't finished.
"But five years ago, you were triple my age then!"
"I suppose in another ten years we'll be the same age," Dad grunted, changing channels.
How old is Mimi?

Answer 1

A + A'.B
= (A + A').(A + B) { AND Distributive Law }
= A + B { (A + A') = 1 }