Решите систему уравнений: (y-1)/(x-1)+(x-1)/(y+1)-4/(xy+x-y-1)=0; (y+2)/(x-2)=(y+4)/(x-3).

\[\left\{ \begin{matrix} \frac{y - 1}{x - 1} + \frac{x - 1}{y + 1} - \frac{x}{xy + x - y - 1} = 0 \\ \frac{y + 2}{x - 2} = \frac{y + 4}{x - 3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ }\]

\[( - 2x + 2)^{2} + x^{2} - 2x - 4 = 0\]

\[4x^{2} - 8x + 4 + x^{2} - 2x - 4 = 0\]

\[5x^{2} - 10 = 0\]

\[5x(x - 2) = 0\]

\[x = 0\]

\[x - 2 = 0;\ \ \ \ \ x = 2.\]

\[y = - 2 \cdot 0 + 2 = 0 + 2 = 2\]

\[y = - 2 \cdot 2 + 2 = - 4 + 2 = - 2.\]

\[Ответ:(0;2),\ (2;\ - 2).\]