117. \(\left(\frac{1}{a-b}-\frac{1}{a+b}\right):\frac{2}{a-b}\)

\(\frac{1}{a-b}-\frac{1}{a+b}=\frac{2b}{(a-b)(a+b)}\).

\(\frac{2b}{(a-b)(a+b)}:\frac{2}{a-b}=\frac{2b}{(a-b)(a+b)}\cdot\frac{a-b}{2}=\frac{b}{a+b}\).

Ответ: \(\frac{b}{a+b}\).