A³-b³ . (a+b+a-b): a²+ab+b²=? ------- ------------ ---------------- 2a+2b (a-b+a+b) :...

Решите задачу:

$\frac{ {a}^{3} - {b}^{3} }{2a + 2b} \times \frac{(a + b + a - b)}{(a - b + a + b)} \div \frac{ {a}^{2} + ab + {b}^{2} }{ {a}^{2} - {b}^{2} } = \frac{ ({a}^{3} - {b}^{3}) \times (a - b + a + b) \times (a + b)(a - b) }{2(a + b) \times (a - b + a + b) \times ({a}^{2} + ab + {b}^{2}) } = \frac{(a - b)( {a}^{2} + ab + {b}^{2}) \times (a - b)}{2 \times ( {a}^{2} + ab + {b}^{2}) } = \frac{(a - b) \times (a - b)}{2} = \frac{ {(a - b})^{2} }{2} = \frac{ {a}^{2} - 2ab + {b}^{2} }{2}$