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Answer:
1/xyz (x^2+y^2+z^2)+2 (1/x+1/y+1/z)
=(x^2+y^2×z^2)/xyz+2 (yz+xz+xy)/xyz
=(x^2+y^2+z^2)/xyz+(2yz+2xz+2xy)/xyz
=(x^2+y^2+z^2+2yz+2xz+2xy)/xyz
=(x+y+z)^2/xyz