Bài giải:

$\frac{{{x}^{2}}(y-z)+{{y}^{2}}(z-x)+{{z}^{2}}(x-y)}{{{x}^{2}}y-{{x}^{2}}z+{{y}^{2}}z-{{y}^{3}}}$= $\frac{{{x}^{2}}y-{{x}^{2}}z+{{y}^{2}}z-{{y}^{2}}x+{{z}^{2}}x-{{z}^{2}}y}{{{x}^{2}}(y-z)+{{y}^{2}}(z-y)}$

= $\frac{({{x}^{2}}y-x{{y}^{2}})+({{z}^{2}}x-{{z}^{2}}y)-({{x}^{2}}z-{{y}^{2}}z)}{({{x}^{2}}-{{y}^{2}})(y-z)}$ = $\frac{xy(x-y)+{{z}^{2}}(x-y)-z(x-y)(x+y)}{(x-y)(x+y)(y-z)}$

= $\frac{(xy+{{z}^{2}}-zx-zy)(x-y)}{(x-y)(x+y)(y-z)}$ = $\frac{(x-y)(y-z)(x-z)}{(x-y)(x+y)(y-z)}=\frac{x-z}{x+y}$

Vậy đáp án đúng là: A