\(\left\{{}\begin{matrix}\sqrt{\frac{x+3}{x}}+\frac{2y}{y-2}=8\left(1\right)\\2\sqrt{\frac{x+3}{x}}+\frac{3y}{y-2}=13\left(2\right)\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\frac{3}{2}\sqrt{\frac{x+3}{x}}+\frac{3y}{y-2}=12\\2\sqrt{\frac{x+3}{x}}+\frac{3y}{y-2}=13\end{matrix}\right..\text{Trừ vế theo vế ta được:}\frac{1}{2}\sqrt{\frac{x+3}{x}}=1\Leftrightarrow\sqrt{\frac{x+3}{x}}=2\Leftrightarrow\frac{x+3}{x}=4\Leftrightarrow x+3=4x\Leftrightarrow x=1.\text{ Thay x=1 vào}\left(1\right)taduoc:2+\frac{2y}{y-2}=8\Leftrightarrow\frac{2y}{y-2}=6\Leftrightarrow2y=6y-12\Leftrightarrow y=3\)
thử lại ta thấy t/m. Vậy: x=1;y=3
