\[\boxed{\text{969.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[\frac{x^{2} + x - 5}{x - 1} =\]
\[= \frac{x^{2} - 2x + 1 + 3x - 6}{x - 1} =\]
\[= \frac{(x - 1)^{2} + 3 \cdot (x - 2)}{x - 1} =\]
\[= \frac{(x - 1)^{2} + 3 \cdot (x - 1 - 1)}{x - 1}\]
\[при\ \ x = 1 - \sqrt{3} \Longrightarrow x -\]
\[- 1 = - \sqrt{3}:\]
\[\frac{\left( - \sqrt{3} \right)^{2} + 3 \cdot \left( - \sqrt{3} - 1 \right)}{- \sqrt{3}} =\]
\[= \frac{3 - 3\sqrt{3} - 3}{- \sqrt{3}} = - \frac{3\sqrt{3}}{- \sqrt{3}} = 3.\]