Question

Выполните Действие
Выполните Действие ​

Answer 1

$\frac{ {x}^{3} + 5 {x}^{2} - x - 5}{ {x}^{2} - 25 } \div (x + 1)$

${x}^{3} + 5 {x}^{2} - x - 5 = x( {x}^{2} - 1) + 5( {x}^{2} - 1) = ( {x}^{2} - 1)(x + 5)$

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${x}^{2} - 25$

${x}^{2} - 25 = 0$

$x{1} = 5$

$x{2} = - 5$

${x}^{2} - 25 = (x + 5)(x - 5)$

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$\frac{( {x}^{2} - 1)(x + 5)}{(x + 5)(x - 5)} \div (x + 1) = \frac{ {x}^{2} - 1}{x - 5} \times \frac{1}{x + 1} = \frac{ {x}^{2} - 1 }{(x - 5)(x + 1)} = \frac{ {x}^{2} - 1}{ {x}^{2} + x - 5x - 5} = \frac{ {x}^{2} - 1}{ {x}^{2} - 4x - 5 }$

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${x}^{2} - 4x - 5 = 0$

D=36

$x {1} = \frac{4 + 6}{2} = 5$

$x{2} = \frac{4 - 6}{2} = - 1$

${x}^{2} - 4x - 5 = (x + 5)(x - 1)$

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${x}^{2} - 1 = 0$

$x{1} = 1$

$x{2} = - 1$

${x}^{2} - 1 = (x + 1)(x - 1)$

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$\frac{(x + 1)(x - 1)}{(x + 5)(x - 1)} = \frac{x + 1}{x + 5}$