\(x:y:z=5:4:3\Rightarrow\dfrac{x}{5}=\dfrac{y}{4}=\dfrac{z}{3}=\left\{{}\begin{matrix}\dfrac{x+2y-3z}{5+2.4-3.3}=\dfrac{x+2y-3z}{4}\\\dfrac{x-2y+3z}{5-2.4+3.3}=\dfrac{x-2y+3z}{6}\end{matrix}\right.\)
\(\Rightarrow A=\dfrac{x+2y-3z}{x-2y+3z}=\dfrac{6}{4}=\dfrac{3}{2}\)