\(\left\{{}\begin{matrix}\dfrac{2}{x+y}+\dfrac{1}{x-y}=3\\\dfrac{1}{x+y}-\dfrac{3}{x-y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x+y}+\dfrac{4}{x-y}=2\\\dfrac{1}{x+y}-\dfrac{3}{x-y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{7}{x-y}=1\\\dfrac{2}{x+y}+\dfrac{1}{x-y}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{7}{x-y}=1\\\dfrac{14}{x+y}+\dfrac{7}{x-y}=21\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{14}{x+y}=20\\\dfrac{7}{x-y}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}20x+20y=14\\x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}20x+20y=14\\20x-20y=140\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}40x=154\\x-y=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{77}{20}\\y=-\dfrac{63}{20}\end{matrix}\right.\)
