Simplifying Boolean algebra... What am I missing?

Question

I'm reviewing boolean algebra, but I'm having trouble with a basic simplification: $$\begin{equation}\begin{aligned} &x'z'+ xyz +xz'\\ &= z'(x+x')+xyz\\ &= z'+xyz\\ &= ??? \\ &= z'+xy \end{aligned}\end{equation}\tag{2}\label{eq2}$$

I can't seem to find a theorem or postulate that satisfies the final step in any table. What is it that I'm not seeing?

Answer 1

You have

\begin{eqnarray*}z'+xyz & = & z'(1+xy) + xyz \\ & = & (z'+z)xy + z'\\ & = & z' + xy \end{eqnarray*}