Question

( \frac{ a }{ a-b } - \frac{ a ^ { } }{ a+b } ) \frac{ a+b }{ 2b } ​

Answer 1

Ответ:

$(\frac{a}{a-b}-\frac{a}{a+b})*\frac{a+b}{2b}=\frac{a}{a-b}$

$1)\frac{a}{a-b}-\frac{a}{a+b} =\frac{a(a+b)-a(a-b)}{(a-b)(a+b)}=\frac{a^{2}+ab-a^{2}+ab }{(a-b)(a+b)}=\frac{2ab}{(a-b)(a+b)}$

$2)\frac{2ab}{(a-b)(a+b)}*\frac{a+b}{2b}=\frac{2ab*(a+b)}{(a-b)(a+b)*2b}=\frac{a}{a-b}$