Выполните действия: (2a/b^2-1/2a):(1/b+1/2a).

Ответ:

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

\[1.\ \ \frac{2a^{\backslash 2a}}{b^{2}} - \frac{1\hat{}\backslash b^{2}}{2a} = \frac{4a^{2} - b^{2}}{2ab^{2}}\]

\[2.\ \ \ \frac{1^{\backslash 2a}}{b} + \frac{1^{\backslash b}}{2a} = \frac{2a + b}{2ab}\]

\[3.\ \ \ \frac{4a^{2} - b^{2}}{2ab^{2}}\ :\frac{2a + b}{2ab} =\]

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

\[= \frac{2a - b}{b}\]