\(x+y+z=0\)
\(\Rightarrow x+y=-z\)
\(\Rightarrow x^2+y^2-z^2=-2xy\)
Tương tự: \(\left\{{}\begin{matrix}y^2+z^2-x^2=-2yz\\z^2+x^2-y^2=-2zx\end{matrix}\right.\)
\(A=\dfrac{xy}{x^2+y^2-z^2}+\dfrac{yz}{y^2+z^2-x^2}+\dfrac{zx}{z^2+x^2-y^2}\)
\(=-\left(\dfrac{xy}{2xy}+\dfrac{yz}{2yz}+\dfrac{zx}{2zx}\right)=-\dfrac{3}{2}\)