ĐKXĐ: \(x\ne-1;y\ne3\)
\(\left\{{}\begin{matrix}\dfrac{5x+1}{x+1}+\dfrac{y+3}{y-3}=27\\\dfrac{2x}{x+1}-\dfrac{2y}{y-3}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{5\left(x+1\right)-4}{x+1}+\dfrac{y-3+6}{y-3}=27\\\dfrac{2\left(x+1\right)-2}{x+1}-\dfrac{2\left(y-3\right)+6}{y-3}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}5-\dfrac{4}{x+1}+1+\dfrac{6}{y-3}=27\\2-\dfrac{2}{x+1}-2-\dfrac{6}{y-3}=4\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-\dfrac{4}{x+1}+\dfrac{6}{y-3}=21\\-\dfrac{2}{x+1}-\dfrac{6}{y-3}=4\end{matrix}\right.\)
Đặt \(\left\{{}\begin{matrix}\dfrac{1}{x+1}=u\\\dfrac{1}{y-3}=v\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}-4u+6v=21\\-2u-6v=4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}u=-\dfrac{25}{6}\\v=\dfrac{13}{18}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{x+1}=-\dfrac{25}{8}\\\dfrac{1}{y-3}=\dfrac{13}{18}\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x+1=-\dfrac{8}{25}\\y-3=\dfrac{18}{13}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{33}{25}\\y=\dfrac{57}{13}\end{matrix}\right.\)
