[Math] Simplify a boolean algebra expression: xy + xz’ + x’yz

Question

I need to simplify xy + xz' + x'yz into xz' + yz. I know that these expressions are equal in truth value, but I'm not sure how to simplify the first to get the second.

Here are the steps I can do:
1) xy + xz' + x'yz
2) y(x + x'z) + xz'
3) y((x + x')(x + z)) + xz'
4) y(x + z) + xz'

But that is where I get stuck. Any help you can give me would be great. Thanks.

Answer 1

$xy+xz'+x'yz$
$=(xyz+xyz')+(xyz'+xy'z')+x'yz$
$=xyz+(xyz'+xy'z')+x'yz$
$=xyz+xz'+x'yz$
$=(x+x')yz+xz'$
$=xz'+yz$