Proof writing involving Boolean algebra: AB' + AC + BC How? 
AB' + AC + BC ≡ AB' + BC
RS
≡ AB' + AC + BC
≡(AB' + A)(C + BC)
≡ AC
Am I missing something? Thanks.

A quick test with truth values would show that what you have cannot be right: if $A$ is false and $C$ is true, $AC$ is false, but $AB'+BC$ is true when $B$ is true.
$$\begin{align*}
AB'+AC+BC&\equiv AB'+A(B+B')C+BC\\
&\equiv AB'+ABC+AB'C+BC\\
&\equiv(AB'+AB'C)+(ABC+BC)\\
&\equiv AB'+BC
\end{align*}$$
