\(\sqrt{\dfrac{x}{y}}=\dfrac{3}{4}\Rightarrow\dfrac{x}{y}=\dfrac{9}{16}\Rightarrow\dfrac{x}{9}=\dfrac{y}{16}\)
Đặt \(\dfrac{x}{9}=\dfrac{y}{16}=k\Rightarrow x=9k;y=16k\)
\(A=\dfrac{4x-5y}{3x+4y}=\dfrac{4.9k-5.16k}{3.9k+4.16k}=\dfrac{36k-80k}{27k+64k}=\dfrac{-44k}{91k}=\dfrac{-44}{91}\)
