Заданик #1.
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Задание #2.
[tex] \frac{ {x}^{2} - 8x - 9 }{ {x}^{2} + 9x + 8 } = \frac{ {x}^{2} + x - 9x - 9 }{ {x}^{2} + x + 8x + 8 } = \frac{x(x + 1) - 9(x + 1)}{x(x + 1) + 8(x + 1)} = \frac{(x + 1)(x - 9)}{(x + 1)(x + 8)} = \frac{x - 9}{x + 8} [/tex]
[tex] \frac{ {x}^{2} - 8x + 15 }{ - {x}^{2} + 5x - 6} = \frac{ {x}^{2} - 5x - 3x + 15}{ - ( {x}^{2} - 5x + 6) } = \frac{x(x - 5) - 3(x - 5)}{ - ( {x}^{2} - 3x - 2x + 6) } = \frac{(x - 5)(x - 3)}{ - (x(x - 3) - 2(x - 3))} = \frac{(x - 5)(x - 3)}{ - (x - 3)(x - 2)} = \frac{x - 5}{2 - x} [/tex]
Задание #3.
[tex] \frac{5x + 1}{ {x}^{2} + 9x - 10} \div \frac{5 {x}^{2} + x }{ {x}^{2} - 2x + 1} = \frac{5x + 1}{ {x}^{2} - x + 10x - 10 } \times \frac{ {(x - 1)}^{2} }{x(5x + 1)} = \frac{5x + 1}{x(x - 1) + 10(x - 1)} \times \frac{ {(x - 1)}^{2} }{x(5x + 1)} = \frac{5x + 1}{(x - 1)(x + 10)} \times \frac{ {(x - 1)}^{2} }{x(5x + 1)} = \frac{x - 1}{(x + 10)x} = \frac{x - 1}{ {x}^{2} + 10x } [/tex]
