Сократить дробь: (3x^2-16x+5)/(-4x^2+x^3-5x).

Ответ:

\[\frac{3x^{2} - 16x + 5}{- 4x^{2} + x^{3} - 5x} =\]

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

\[1)\ 3x^{2} - 16x + 5 =\]

\[= 3\left( x - \frac{1}{3} \right)(x - 5) =\]

\[= (3x - 1)(x - 5)\]

\[D_{1} = 64 - 15 = 49\]

\[x_{1} = \frac{8 + 7}{3} = 5;\ \]

\[x_{2} = \frac{8 - 7}{3} = \frac{1}{3}.\]

\[2) - 4x^{2} + x^{3} - 5x =\]

\[= x\left( x^{2} - 4x - 5 \right) =\]

\[= x(x - 5)(x + 1)\]

\[D_{1} = 4 + 5 = 9\]

\[x_{1} = 2 + 3 = 5;\]

\[x_{2} = 2 - 3 = - 1.\]