Gọi : \(\left\{{}\begin{matrix}\frac{1}{x-2}=a\\\frac{1}{y-1}=b\end{matrix}\right.\left(x\ne2;y\ne1\right)\)
Vậy hpt ban đầu biến thành:
\(\left\{{}\begin{matrix}a+b=2\\2a-3b=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=\frac{7}{5}\\b=\frac{3}{5}\end{matrix}\right.\)
Ta có: \(\left\{{}\begin{matrix}a=\frac{1}{x-2}=\frac{7}{5}\Leftrightarrow x=\frac{19}{7}\\b=\frac{1}{y-1}=\frac{3}{5}\Leftrightarrow y=\frac{8}{3}\end{matrix}\right.\)
Vậy: hpt có nghiệm là: \(\left(x;y\right)=\left(\frac{19}{7};\frac{8}{3}\right)\)
