Is it possible, in Boolean Algebra, to add arbitrarily a new term to both sides of an expression?

Question

First of all, i'm sorry for my english. I'll try to do my best to explain myself.

I've been trying to look for it on the internet, but i'm not sure about the answer. I hope someone can help me here :)

My question is: Is it possible to add a new term to both sides of a boolean algebra expression?

For example:

A * B' = 0, then

A * B' + A = 0 + A, then

A * B' + A = A

I know that in that equation specifically DOES work, but i'm not sure if it's absolutely acceptable always.

Thank you!

Answer 1

If $A=B$ then $A+C = B+C$, but it's not generally true in Boolean algebras that if $A+C=B+C$ then $A=B$.