Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 801

\[1)\ \frac{3x - 1}{x + 2} - \frac{7}{2 + x} =\]

\[= \frac{7x^{2} - 28}{x^{2} - 4} + \frac{18}{2 - x}\]

\[(3x - 8)(x - 2) =\]

\[= 7x^{2} - 28 - 18(x + 2)\]

\[3x^{2} - 6x - 8x + 16 =\]

\[= 7x^{2} - 28 - 18x - 36\]

\[3x^{2} - 14x + 16 =\]

\[= 7x^{2} - 18x - 64\]

\[4x^{2} - 4x - 80 = 0\]

\[x^{2} - x - 20 = 0\]

\[D = 1 + 80 = 81\]

\[x_{1} = \frac{1 - 9}{2} = - 4;\]

\[x_{2} = \frac{1 + 9}{2} = 5.\]

\[Ответ:\ - 4;\ 5.\]

\[2)\ \frac{x + 1}{x + 3} - \frac{12}{x^{2} - 9} = \frac{2 - x}{3 - x}\]

\[(x + 1)(x - 3) - 12 =\]

\[= (x - 2)(x + 3)\]

\[x^{2} - 3x + x - 3 - 12 =\]

\[= x^{2} + 3x - 2x - 6\]

\[x^{2} - 2x - 15 = x^{2} + x - 6\]

\[3x = - 9\]

\[x = - 3.\]

\[Ответ:\ \ корней\ нет.\]