Reducing a Boolean function

Question

I have the following boolean function:

f(x,y,z) = xyz + xyz' + xy'z + x'yz + xy'z'

I could reduce it to the following:

f(x,y,z) = xy + xy'z + x'yz + xy'z

Im not sure what to do next, i know it can be reduced to x + yz but im really lost.

Thanks for the help and im sorry if im not using the traditional notations

Answer 1

$$\begin{align*} \color{red}{xyz+xyz'}+\color{blue}{xy'z}+x'yz+\color{blue}{xy'z'}&=\color{red}{xy(z+z')}+\color{blue}{xy'(z+z')}+x'yz\\ &=xy+xy'+x'yz\\ &=x(y+y')+x'yz\\ &=x+x'yz\\ &\overset{*}=(x+xyz)+x'yz\\ &=x+(x+x')yz\\ &=x+yz \end{align*}$$

The starred step uses one of the absorption rules: $x=x+xu$ for any $u$.