Сократите дробь (9x^2-6x-8)/(6x^2-5x-4).

Ответ:

\[\frac{9x^{2} - 6x - 8}{6x^{2} - 5x - 4}\]

\[1)\ 9x^{2} - 6x - 8 = 9 \cdot \left( x - \frac{4}{3} \right)\left( x + \frac{2}{3} \right) =\]

\[= (3x - 4)(3x + 2)\]

\[D = 9 + 72 = 81\]

\[x_{1} = \frac{3 + 9}{9} = \frac{12}{9} = \frac{4}{3};\]

\[x_{2} = \frac{3 - 9}{9} = - \frac{6}{9} = - \frac{2}{3}.\]

\[2)\ 6x^{2} - 5x - 4 = 6 \cdot \left( x - \frac{4}{3} \right)\left( x + \frac{1}{2} \right) =\]

\[= (3x - 4)(2x + 1)\]

\[D = 25 + 96 = 121\]

\[x_{1} = \frac{5 + 11}{12} = \frac{16}{12} = \frac{4}{3};\]

\[x_{2} = \frac{5 - 11}{12} = - \frac{6}{12} = - \frac{1}{2}.\]

\[\frac{9x^{2} - 6x - 8}{6x^{2} - 5x - 4} = \frac{(3x - 4)(3x + 2)}{(3x - 4)(2x + 1)} =\]

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