Упростить: (1/a-1/b):(b^2-a^2)/(ab^2).

Ответ:

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

\[= \frac{b - a}{\text{ab}} \cdot \frac{ab^{2}}{b^{2} - a^{2}} =\]

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