\(x+y-z=ax+by+2cz-\left(ax+by\right)=2cz\)
\(\Rightarrow x+y+z=2z\left(c+1\right)\)
\(\Rightarrow\dfrac{1}{c+1}=\dfrac{2z}{x+y+z}\)
Tương tự: \(\dfrac{1}{a+1}=\dfrac{2x}{x+y+z}\) ; \(\dfrac{1}{b+1}=\dfrac{2y}{x+y+z}\)
\(\Rightarrow A=\dfrac{2x}{x+y+z}+\dfrac{2y}{x+y+z}+\dfrac{2z}{x+y+z}=2\)