Simplifying a boolean expression I need to prove:

XY + ~XZ + YZ = XY + ~XZ

I cannot think how to do this. 

I have tried factorising, but I just don't know of any rule that removes one of the terms like above. 

I start with the LHS, naturally: 

All I can do is get to:

Y(X+Z) + ~XZ
Here is an ugly solution, found with the Karnaugh table and the equation : A = A.B + A./B

XY + /XZ + YZ

= X.Y.Z + X.Y./Z + /X.Y.Z + /X./Y.Z + X.Y.Z + /X.Y.Z

(removing two redundant terms)

= X.Y.Z + X.Y./Z + /X./Y.Z + /X.Y.Z

= XY + /X.Z