Đáp án:
` A=1`
Giải thích các bước giải:
` 1/x+1/y+1/z=0`
`->xy+yz+zx=0`
`->yz=-zx-xy`
`->x^2+2yz=x^2+yz-zx-xy=x(x-y)-z(x-y)=(x-z)(x-y)`
*)Cmtt: `y^2+2xz=(y-x)(y-z);z^2+2xy=(z-x)(z-y)`
`->A=(yz)/((x-z)(x-y))+(xz)/((y-x)(y-z))+(xy)/((z-x)(z-y))`
`->A=(yz)/((x-z)(x-y))+(xz)/((x-y)(z-y))-(xy)/((x-z)(z-y))`
`->A=(yz(z-y))+(xz(x-z))-(xy(x-y))/((x-y)(x-z)(z-y))`
Đặt `B=yz(z-y)+xz(x-z)-xy(x-y)`
`=yz^2-y^2z+z^2z-xz^2-x^2y+xy^2`
`=x^2z-xyz-z^2x+yz^2-x^2y+xy^2+xyz-y^2z`
`=z(x^2-xy-zx+yz)-y(x^2-xy-xz+yz)`
`=(z-y)[x(x-y)-z(x-y)]`
`=(z-y)(x-z)(x-y)`
`->A=((z-y)(x-z)(x-y))/((x-y)(x-z)(z-y))=1`