How do I simplify this boolean function using the rules of boolean algebra?

[Ownaginatious]

Okay, so I'm stuck at a step of a much bigger problem where I have to simplify a boolean function.

Homework Statement

Here is where I'm stuck, I have to change the left hand side to the right hand side. How do I prove this with the rules of boolean algebra?

CA + CB + B'A = CB + B'A

Homework Equations

The Attempt at a Solution

The above is as far as I've gotten (as I said, this was taken from a bigger problem).

Can someone please show me the steps that will change the left hand side of the equation to the right? According to truth tables, they are infact equal.

 

[elduderino]

This appears wrong as the expression you wrote implies A+B=B, which is not true for a complete truth table.

 

[Ownaginatious]

Well, according to this truth table, it's right:

http://img170.imageshack.us/img170/3023/truth.png

I can't figure out how to prove this algebraically though.