Ответ:
1)
[tex] \frac{y + 2}{y - 2} [/tex]
2)
[tex] \frac{8x + 22}{5 - x} [/tex]
Пошаговое объяснение:
[tex] \frac{y {}^{2} + 8y }{4 - y {}^{2} } - \frac{4y - 4}{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 8y - 4y + 4 }{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 4y + 4}{4 - y {}^{2} } = \\ = - \frac{y {}^{2} + 4y + 4}{y {}^{2} - 4 } = \\ = - \frac{(y + 2) {}^{2} }{y {}^{2} - 2 {}^{2} } = \\ = - \frac{(y + 2) {}^{2} }{(y - 2)(y + 2)} = \\ = - \frac{y + 2}{y - 2} [/tex]
[tex] \frac{5x + 6}{5 - x} + \frac{3x + 16}{5 - x} = \\ = \frac{5x + 6 + 3x + 16}{5x - 6} = \\ = \frac{8x + 22}{5 - x} [/tex]
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Answers & Comments
Ответ:
1)
[tex] \frac{y + 2}{y - 2} [/tex]
2)
[tex] \frac{8x + 22}{5 - x} [/tex]
Пошаговое объяснение:
1)
[tex] \frac{y {}^{2} + 8y }{4 - y {}^{2} } - \frac{4y - 4}{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 8y - 4y + 4 }{4 - y {}^{2} } = \\ = \frac{y {}^{2} + 4y + 4}{4 - y {}^{2} } = \\ = - \frac{y {}^{2} + 4y + 4}{y {}^{2} - 4 } = \\ = - \frac{(y + 2) {}^{2} }{y {}^{2} - 2 {}^{2} } = \\ = - \frac{(y + 2) {}^{2} }{(y - 2)(y + 2)} = \\ = - \frac{y + 2}{y - 2} [/tex]
2)
[tex] \frac{5x + 6}{5 - x} + \frac{3x + 16}{5 - x} = \\ = \frac{5x + 6 + 3x + 16}{5x - 6} = \\ = \frac{8x + 22}{5 - x} [/tex]