Question

Срочно!!! 35 баллов!!!Решите по действиям!!!

Answer 1

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

Answer 2

$1)\frac{a+b}{a-b}-\frac{a-b}{a+b}=\frac{(a+b)^{2}-(a-b)^{2}}{(a-b)(a+b)}=\frac{a^{2}+2ab+b^{2}-a^{2}+2ab-b^{2}}{(a-b)(a+b)}=\frac{4ab}{(a-b)(a+b)}\\\\2)\frac{(a-b)^{2}}{4ab}=\frac{(a-b)(a-b)}{4ab}\\\\3)\frac{4ab}{(a-b)(a+b)}*\frac{(a-b)(a-b)}{4ab}=\frac{a-b}{a+b}\\\\Otvet:\boxed{\frac{a-b}{a+b}}$