ĐKXĐ: \(x\ne1;y\ne-2\)
\(\left\{{}\begin{matrix}\dfrac{x+1}{x-1}+\dfrac{3y}{y+2}=7\left(1\right)\\\dfrac{2}{x-1}-\dfrac{5}{y+2}=4\left(2\right)\end{matrix}\right.\)
\(\left(1\right)\Rightarrow\dfrac{x+1}{x-1}-1+\dfrac{3y}{y+2}-3=7-4\)
\(\Rightarrow\dfrac{x+1-x+1}{x-1}+\dfrac{3y-3y-6}{y+2}=3\)
\(\Rightarrow\dfrac{2}{x-1}-\dfrac{6}{y+2}=3\left(3\right)\)
Đặt: \(a=\dfrac{2}{x-1};b=\dfrac{1}{y+2}\), Từ (3) và (2) Ta có hệ pt:
\(\left\{{}\begin{matrix}a-6b=3\\a-5b=4\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=9\\b=1\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{2}{x-1}=9\\\dfrac{1}{y+2}=1\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\dfrac{11}{9}\\y=-1\end{matrix}\right.\)
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