Question

simplify the given question​

Answer 1

Answer:

$\frac{2}{a + 4}$

Step-by-step explanation:

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