Suppose x, y, and z are nonzero complex numbers such that (x+y+z)\left(x^{2}+y^{2}+z^{2}\right)=x^{3}+y^{3}+z^{3}. Compute
(x+y+z)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)
Suppose x, y, and z are nonzero complex numbers such that (x+y+z)\left(x^{2}+y^{2}+z^{2}\right)=x^{3}+y^{3}+z^{3}. Compute