\[\frac{x^{2} - 5}{x - 1} = \frac{7x + 10}{9}\ \ | \cdot 9(x - 1);x \neq 1\]
\[9\left( x^{2} - 5 \right) = (7x + 10)(x - 1)\]
\[9x^{2} - 45 = 7x^{2} + 10x - 7x - 10\]
\[9x^{2} - 7x^{2} - 3x - 45 + 10 = 0\]
\[2x^{2} - 3x - 35 = 0\]
\[D = 9 + 280 = 289 = 17^{2}\]
\[x_{1} = \frac{3 + 17}{4} = 5;\]
\[x_{2} = \frac{3 - 17}{4} = - \frac{14}{4} = - 3,5.\]
\[Ответ:x = - 3,5;x = 5.\]