ĐKXĐ: \(x\ne\pm y\)
\(\left\{{}\begin{matrix}\dfrac{108}{x+y}+\dfrac{63}{x-y}=4\\\dfrac{81}{x+y}+\dfrac{84}{x-y}=7\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}\dfrac{432}{x+y}+\dfrac{252}{x-y}=16\\\dfrac{243}{x+y}+\dfrac{252}{x-y}=21\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{432}{x+y}+\dfrac{252}{x-y}-\dfrac{243}{x+y}-\dfrac{252}{x-y}=16-21=-5\\\dfrac{81}{x+y}+\dfrac{84}{x-y}=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}\dfrac{189}{x+y}=-5\\\dfrac{84}{x-y}=7-\dfrac{81}{x+y}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+y=-37,8\\\dfrac{84}{x-y}=7-\dfrac{81}{-37,8}=\dfrac{64}{7}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+y=-37,8\\x-y=7\cdot\dfrac{84}{64}=\dfrac{147}{16}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x=-37,8+\dfrac{147}{16}=-\dfrac{2289}{80}\\x+y=-37,8\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=-\dfrac{2289}{160}\\y=-\dfrac{3759}{160}\end{matrix}\right.\)
