Упростите выражение: x^2+5x-(2x^2+7x-30)/(x+8)*(x^2+7x-8)/(2x-5).

Ответ:

\[= x^{2} + 5x - (x + 6)(x - 1) =\]

\[= x^{2} + 5x - x^{2} - 6x + x + 6 = 6.\]

\(1)\ 2x^{2} + 7x - 30 =\)

\[= 2(x + 6)\left( x - \frac{5}{2} \right) =\]

\[= (x + 6)(2x - 5)\]

\[D = 49 + 240 = 289\]

\[x_{1} = \frac{- 7 + 17}{4} = \frac{10}{4} = \frac{5}{2};\ \]

\[x_{2} = \frac{- 7 - 17}{4} = - \frac{24}{4} = - 6.\]

\[2)\ x^{2} + 7x - 8 = (x + 8)(x - 1)\]

\[x_{1} + x_{2} = - 7;\ \ x_{1} \cdot x_{2} = - 8\]

\[x_{1} = - 8;\ \ x_{2} = 1.\]