How Do I Simplify This Boolean Expression?

[LF07LAN]

Homework Statement

I have collected all the boolean terms on a circuit and I'm having trouble simplifying the following section of the circuit:

Key:
Not is !
OR is +
AND is *

I started with !( (A*!B)*(A+C) ) and used demorgans to get

(!A+B) + (!A*!C)


I cannot see beyond the parenthesis and do not know which rules to apply to maintain order

Please can someone help with a little workthrough

Thanks in advance,
Lee

 

[MisterX]

(!A+B) + (!A*!C)

The first set of parenthesis is unnecessary.

Next, you can use one of the absorption rules.

!A!C is only true when !A is true. !A!C is false when !A is false.

 

[LF07LAN]

So that was it. I just couldn't see past the parenthesis and didn't know where to apply the associative rule.

So the simple answer is !A+B

This is only part of the whole circuit so I should be able to go on and do the rest

Thanks