Сократите дробь (10x^2+9x-9)/(6x^2+11x+3).

Ответ:

\[\frac{10x^{2} + 9x - 9}{6x^{2} + 11x + 3}\]

\[1)\ 10x^{2} + 9x - 9 = 10 \cdot \left( x - \frac{3}{5} \right)\left( x + \frac{3}{2} \right) =\]

\[= (5x - 3)(2x + 3)\]

\[D = 81 + 360 = 441\]

\[x_{1} = \frac{- 9 + 21}{20} = \frac{12}{20} = \frac{3}{5}\]

\[x_{2} = \frac{- 9 - 21}{20} = - \frac{30}{20} = - \frac{3}{2}\]

\[2)\ 6x^{2} + 11x + 3 = 6 \cdot \left( x + \frac{3}{2} \right)\left( x + \frac{1}{3} \right) =\]

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

\[D = 121 - 72 = 49\]

\[x_{1} = \frac{- 11 - 7}{12} = - \frac{18}{12} = - \frac{3}{2}\]

\[x_{2} = \frac{- 11 + 7}{12} = - \frac{4}{12} = - \frac{1}{3}\]

\[\frac{10x^{2} + 9x - 9}{6x^{2} + 11x + 3} = \frac{(5x - 3)(2x + 3)}{(2x + 3)(3x + 1)} = \frac{5x - 3}{3x + 1}.\]