Question

Докажите тождество!!

Answer 1

Объяснение:

$1) \: ( \frac{8a}{4 - {a}^{2} } - \frac{a - 2}{a + 2} ) \div \frac{a + 2}{a} + \frac{2}{a - 2} = - 1 \\ 1. \: \frac{8a}{4 - {a}^{2} } - \frac{a - 2}{a + 2} = \frac{8a - 2a + {a}^{2} + 4 + - 2a}{(2 - a)(2 + a)} = \frac{ {a}^{2} + 4a + 4}{(2 - a)(2 + a)} = \frac{(a + 2)^{2} }{(2 - a)(2 + a)} = \frac{a + 2}{2 - a} \\ 2. \: \frac{a + 2}{2 - a} \div \frac{a + 2}{a} = \frac{a + 2}{2 - a} \times \frac{a}{a + 2} = \frac{a}{2 - a} \\ 3. \: \frac{a}{2 - a} + \frac{2}{a - 2} = ( - \frac{a}{a - 2} ) + \frac{2}{a - 2} = \frac{ - (a - 2)}{a - 2} = - 1$