Решите уравнение: (x^2-5)/(x-1)=(7x+10)/9.

Ответ:

\[\frac{x^{2} - 5}{x - 1} = \frac{7x + 10}{9}\ \ | \cdot 9(x - 1);x \neq 1\]

\[9\left( x^{2} - 5 \right) = (7x + 10)(x - 1)\]

\[9x^{2} - 45 = 7x^{2} + 10x - 7x - 10\]

\[9x^{2} - 7x^{2} - 3x - 45 + 10 = 0\]

\[2x^{2} - 3x - 35 = 0\]

\[D = 9 + 280 = 289 = 17^{2}\]

\[x_{1} = \frac{3 + 17}{4} = 5;\]

\[x_{2} = \frac{3 - 17}{4} = - \frac{14}{4} = - 3,5.\]

\[Ответ:x = - 3,5;x = 5.\]