Упростите выражение: ((b+1)/(b-1)-b/(b+1)):(3b+1)/(2b-2).

\[\left( \frac{b + 1^{\backslash b + 1}}{b - 1} - \frac{b^{\backslash b - 1}}{b + 1} \right)\ :\frac{3b + 1}{2b - 2} =\]

\[= \frac{b^{2} + 2b + 1 - b^{2} + b}{(b - 1)(b + 1)} \cdot \frac{2b - 2}{3b + 1} =\]

\[= \frac{(3b + 1) \cdot 2(b - 1)}{(b - 1)(b + 1)(3b + 1)} =\]

\[= \frac{2}{b + 1}.\]