Решите уравнение (x^2-1)/6-(x-1)/4=3.

Ответ:

\[\frac{x^{2} - 1}{6} - \frac{x - 1}{4} = 3\ \ \ \ \ \ \ \ | \cdot 12\]

\[2 \cdot \left( x^{2} - 1 \right) - 3 \cdot (x - 1) = 36\]

\[2x^{2} - 2 - 3x + 3 - 36 = 0\]

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

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

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

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

\[Ответ:x = 5;\ \ x = - 3,5.\]