So I've done a simplification and I'm unsure as to whether or not my process is right. Line 5 feels wrong to me so could someone tell me if this is the correct way to do it?
$$\begin{align}&x’yz' + x'yz + xyz + x'yz'\\ &=yz(x+x') + x'z'(y+y)\\ &=yz + x'yz'\\ &=y(z+x'z')\\ &=y(z+x')(z+z')\\ &=y(z+x')\end{align}$$
Everything ok. The step $z+x'z'=(z+x')(z+z')$ looks strange because it clashes with numerical habits, but it may seem more natural written as follows: $$A\lor(B\land C)\leftrightarrow(A\lor B)\land(A\lor C)$$ or equivalently (by De Morgan laws) $$P\land(Q\lor R)\leftrightarrow(P\land Q)\lor(P\land R).$$ These are the distributivity of each of the two laws with respect to the other one. The latter doesn't "clash" when rewritten $$p\left(q+r\right)=pq+pr.$$