Question

Спростіть вираз.....​

Answer 1

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