\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\) suy ra xy + yz + xz = 0
Ta có : x2 + 2yz = x2 + 2yz - xy - yz - xz = x2 + yz - xy - xz = ( x -y ) ( x - z )
Tương tự : y2 + 2xz = ( y - x ) ( y - z ) ; x2 + 2zy = ( x - z ) ( x - y )
\(\Rightarrow A=\frac{yz}{\left(x-y\right)\left(x-z\right)}+\frac{xz}{\left(y-x\right)\left(y-z\right)}+\frac{xy}{\left(x-z\right)\left(x-y\right)}=1\)( tự c/m )