Question

Срочно!! упростите выражение на картинке​

Answer 1

Ответ:

1.

$\frac{ {a}^{2} - 25}{a + 3} \times \frac{1}{ {a}^{2} + 5 a} = \frac{(a - 5)(a + 5)}{a + 3} \times \frac{1}{a(a + 5)} = \\ = \frac{a - 5}{a(a + 3)}$

2.

$\frac{ {a}^{2} + 10a + 25 }{a {}^{3} - 6a {}^{2} + 9 a} \div \frac{a + 5}{a - 3} = \\ = \frac{(a + 5) {}^{2} }{a(a - 3) {}^{2} } \times \frac{a - 3}{a + 5} = \frac{a + 5}{a(a - 3)}$

3.

$\frac{a - 5}{a(a + 3)} - \frac{a + 5}{a(a - 3)} + \frac{16}{ { \alpha }^{2} - 9} = \\ = \frac{a - 5}{a(a + 3)} - \frac{a}{a(a - 3)} + \frac{16}{(a - 3)(a + 3)} = \\ = \frac{(a - 5)(a - 3) - a(a + 3) + 16a}{a(a - 3)(a + 3)} = \\ = \frac{a {}^{2} - 5a - 3a + 15 - {a}^{2} - 3a + 16a}{a(a {}^{2} - 9)} = \\ = \frac{5a + 15}{a( {a}^{2} - 9) } = \frac{5(a + 3)}{a(a - 3)(a + 3)} = \frac{5}{a(a - 3)}$