Question

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Answer 1

ĐKXĐ : \(\left\{{}\begin{matrix}x\ne2\\y\ne1\end{matrix}\right.\)

- Đặt \(\left\{{}\begin{matrix}\dfrac{1}{x-2}=a\\\dfrac{1}{y-1}=b\end{matrix}\right.\)

\(HPTTT\left\{{}\begin{matrix}2a+b=2\\4a-3b=1\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}4a+2b=4\\4a-3b=1\end{matrix}\right.\)

- Trừ hai vế => b = 3/5

=> a = 7/10 .

- Thay lại ta được ; \(\left\{{}\begin{matrix}\dfrac{1}{x-2}=\dfrac{7}{10}\\\dfrac{1}{y-1}=\dfrac{3}{5}\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{24}{7}\\y=\dfrac{8}{3}\end{matrix}\right.\) ( TM )

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