Difficulty simplifying boolean algebra expression

Question

I am simplifying a boolean algebra expression and so far my expression is $$xy + zy + !x*z$$ The answer sheet says the answer is $xy + !x*z$ and when i type in my expression into an online boolean logic calculator it shows the same answer, however i am unable to arrive at the answer. Can anyone help me or give me tips on how do i solve this and also when do i know that a boolean algebra expression can no longer be simplified

Answer 1

Rewrite your expression to:

$$xy + (x + !x)zy + !xz$$

Collect the terms for $x$ and $!x$:

$$x(y + zy) + !x(zy + z)$$

$y+zy$ can be simplified to $y$. Similarly, $zy+z$ can be simplified to $z$.

The resulting expression:

$$xy + !xz$$