Question

Помогите,пожалуйста,с объяснением.
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Сократите:

Answer 1

$( \frac{a - 2b}{ {a}^{2} + 2ab } - \frac{a + 2b}{ {a}^{2} - 2ab} ) \div \frac{4 {b}^{2} }{4 {b}^{2} - {a}^{2} }$
$1) \: \frac{a - 2b}{ a(a + 2b)} - \frac{a + 2b}{ a(a - 2b)} = \frac{(a - 2b)(a - 2b) -(a + 2b)(a + 2b) }{a(a + 2b)(a - 2b)} = \\ \\ = \frac{ {a}^{2} - 2ab - 2ab + 4 {b}^{2} - {a}^{2} - 2ab - 2ab - 4 {b}^{2} }{a(a + 2b)(a - 2b)} = \frac{ - 8ab}{a(a + 2b)(a - 2b)}$
$2) \: \frac{ - 8ab}{a(a + 2b)(a - 2b)} \div \frac{4 {b}^{2} }{4 {b}^{2} - {a}^{2}} = \frac{ - 8ab}{a(a + 2b)(a - 2b)} \times \frac{(2b - a )(2b + a )}{4 {b}^{2} } = \frac{2}{b}$

ОТВЕТ: 2/b