Question

Алгебра. Упростите выражение:

Answer 1

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