Упростите выражение: (6x/(x^2-x-2)+9/(x^2-4))∶(2x+1)/(x^2+3x+2)-(x+13)/(x-2).

Ответ:

\[Дополнительные\ вычисления:\]

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

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

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

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

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

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

\[D = 9 + 16 = 25\]

\[x_{1} = \frac{3 + 5}{4} = 2;\ \ \ \]

\[x_{2} = \frac{3 - 5}{4} = - \frac{2}{4} = - \frac{1}{2}.\]

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

\[= 2 \cdot (x - 2)\left( x + \frac{1}{2} \right) =\]

\[= (x - 2)(2x + 1).\]