Express as a rational expression : [(x^3+y^3+z^3-3xyz)/(a^3+b^3+c^3-3abc)] * [(a^2+b^2+c^2-ab-bc-ca)/(x^2+y^2+z^2-xy-xz-zy)]

Question

Express as a rational expression : [(x^3+y^3+z^3-3xyz)/(a^3+b^3+c^3-3abc)] * [(a^2+b^2+c^2-ab-bc-ca)/(x^2+y^2+z^2-xy-xz-zy)] 
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Reiny · Answer

A long long time ago when I was teaching and we still had time to do some strange mathematics, we compiled a list of unusual factoring patterns.

one of them was this

x^3 + y^3 + z^3 - 3xyz
= (x+y+z)(x^2 + y^2 + z^2 - xy - xz - yz)

isn't that the pattern you see in the second fraction ?

so it should reduce to (x+y+z)/(a+b+c)