x^3+y^3+z^3-3xyz / x+y+z
know how to do with 2 terms e.g. x and y ,but not with 3rd

Factor the top, then do the cancellations.

x^{3}+y^{3}+z^{3}-3xyz=(x+y+z)(x^{2}-x(y+z)+y^{2}-yz+z^{2})