Необходимо упросить данное выражение:​

Ответ:

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

Пошаговое объяснение:

[tex] \small \bigg(1 - \frac{2b}{a + 2b} \bigg): \bigg( \frac{2b - a}{a + 2b} \cdot \big( 1 + \frac{a}{a - 2b} \big) \bigg) = \\ \small = \bigg( \frac{a {+} 2b}{a{ +} 2b} {-} \frac{2b}{a{ +} 2b} \bigg){:} \bigg( \frac{2b {- }a}{a{ + }2b} { \cdot} \Big( \frac{a {-} 2b}{a {- }2b} {+ }\frac{a}{a {-} 2b} \Big) \bigg) = \\ \small = \bigg( \frac{a + 2b - 2b}{a + 2b} \bigg): \bigg( \frac{2b - a}{a + 2b} \cdot \Big( \frac{a - 2b + a}{a - 2b} \Big) \bigg) = \\ \small = \bigg( \frac{a}{a + 2b} \bigg): \bigg( \frac{2b - a}{a + 2b} \cdot \Big( \frac{2a - 2b}{a - 2b} \Big) \bigg) = \\ \small = \bigg( \frac{a}{a + 2b} \bigg): \bigg( \frac{ \cancel{2b - a}}{a + 2b} \cdot \frac{2a - 2b}{ - \cancel{( 2b - a)}} \bigg) = \\ \small = \bigg( \frac{a}{a + 2b} \bigg): \bigg( \frac{ - (2a - 2b)}{a + 2b} \bigg) = \\ \small = \bigg( \frac{a}{a {+} 2b} \bigg){: }\bigg( \frac{ 2b{ - }2a}{a{ + }2b} \bigg) =\frac{a}{ \cancel{a {+ }2b}} \cdot \frac{ \cancel{a {+ }2b}}{ 2b {-} 2a} = \\ = \frac{a}{2b -2a } \\ [/tex]