Bài giải:

 $\frac{1}{x(x-y)(x-z)}+\frac{1}{y(y-z)(y-x)}+\frac{1}{z(z-x)(z-y)}$

= $\frac{-1}{x(x-y)(z-x)}+\frac{-1}{y(y-z)(x-y)}+\frac{-1}{z(z-x)(y-z)}$

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

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

= $\frac{(x-y)\text{ }\!\![\!\!\text{ z(x+y)-}{{\text{z}}^{2}}-xy]}{xyz(x-y)(y-z)(z-x)}$ = $\frac{(x-y)(y-z)(z-x)}{xyz(x-y)(y-z)(z-x)}$ = $\frac{1}{xyz}$

Vậy đáp án đúng là: A