Решебник по алгебре 8 класс Мерзляк Задание 756

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

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

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

\[x_{1} + x_{2} = 6,\ \ x_{1} = 5\]

\[x_{1} \cdot x_{2} = 5,\ \ x_{2} = 1\]

\[2)\ \frac{2x + 12}{x^{2} + 3x - 18} =\]

\[= \frac{2 \cdot (x + 6)}{(x + 6)(x - 3)} = \frac{2}{x - 3}\]

\[x^{2} + 3x - 18 = (x + 6)(x - 3)\]

\[x_{1} + x_{2} = - 3,\ \ x_{1} = - 6\]

\[x_{1} \cdot x_{2} = - 18,\ \ x_{2} = 3\]

\[3)\frac{x^{2} + 9x + 14}{x^{2} + 7x} =\]

\[= \frac{(x + 7)(x + 2)}{x(x + 7)} = \frac{x + 2}{x}\]

\[x^{2} + 9x + 14 = (x + 7)(x + 2)\]

\[x_{1} + x_{2} = - 9,\ \ x_{1} = - 7\]

\[x_{1} \cdot x_{2} = 14,\ \ x_{2} = - 2\]

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