Упростите выражение: a/(a-b):((a+b)/b+b/(a-b)).

\[\frac{a}{a - b}\ :\left( \frac{a + b}{b} + \frac{b}{a - b} \right) = \frac{b}{a}.\]

\[\frac{a + b^{\backslash a - b}}{b} + \frac{b^{\backslash b}}{a - b} =\]

\[= \frac{a^{2} - b^{2} + b^{2}}{b(a - b)} = \frac{a^{2}}{b(a - b)};\]

\[\frac{a}{a - b} \cdot \frac{b(a - b)}{a^{2}} = \frac{b}{a}.\]