Question

\(\left\{{}\begin{matrix}\frac{1}{x+1}+\frac{1-2y}{y}=1\\\frac{x-1}{x+1}-\frac{1}{y}=-4\end{matrix}\right.\)

Giúp t với!!!!!!!!

Answer 1

\(x\ne-1;y\ne0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\frac{1}{x+1}+\frac{1}{y}-2=1\\\frac{x-1}{x+1}-\frac{1}{y}=-4\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\frac{1}{x+1}+\frac{1}{y}=3\\\frac{x-1}{x+1}-\frac{1}{y}=-4\end{matrix}\right.\)

Cộng vế với vế:

\(\frac{x}{x+1}=-1\Leftrightarrow x=-x-1\Rightarrow x=-\frac{1}{2}\)

Thay vào pt dưới:

\(\frac{-\frac{1}{2}-1}{-\frac{1}{2}+1}-\frac{1}{y}=-4\Rightarrow\frac{1}{y}=1\Rightarrow y=1\)

Vậy hệ có 1 cặp nghiệm \(\left(x;y\right)=\left(-\frac{1}{2};1\right)\)