Simplify:

Question

(x * y) + (~x * z) + (y * z)

I'm using ~ to represent NOT, * to represent AND, + to represent OR

I did:

(x * y) + (~x * z) + (y * z) = (x * y) + z(~x * y)
But I can't get any further from here

A boolean algebra calculator online says the simplification to the original expression is : (x * y) + (~x * z) but provides no steps

Another boolean algebra equivalence tester says
(x * y) + (~x * z) + (y * z) is logically equivalent to (x * y) + (~x * z)

Help simplifying (x * y) + (~x * z) + (y * z) would be greatly appreciated.

Answer 1

(x * y) + (~x * z) + (y * z)
(x * y) +z(~x *y)
y+z

Answer 2

How did you get y + z from (x * y) +z(~x *y)?

Answer 3

typo using your symbols. I drew a logic tree.
If x, true=1 if y
If not x, true if y and z
so, true if y and (x or z) Put that into your symbols.