How can I get ~B + AC by simplifying (~A~B)+(AC)+(A~B~C)

Question

The original expression is:

(~A~B~C)+(~A~BC)+(A~B~C)+(A~BC)+(ABC)

I could reduce it to (~A~B)+(AC)+(A~B~C) using the Uniting Law, but I need extra help to finally simplify the expression to ~B+AC

From (~A~B)+(AC)+(A~B~C) I could factor out ~B but then, there's not anything I can simplify.

Thank you.

Answer 1

(~A~B~C)+(~A~BC)+(A~B~C)+(A~BC)+(ABC) =
(~A~B)+(A~B)+(ABC) =
~B+ABC =
~B+AC

or, from your reduction

(~A~B)+(AC)+(A~B~C) =
A(C+~B~C) + ~A~B =
A(C+~B) + ~A~B =
A~B + AC + ~A~B =
~B+AC