Упрощение алгебраических выражений. Задача 26

ОТВЕТ: \({\left( {a-b} \right)^2}\).

\(\left( {{a^2}-{b^2}-\dfrac{{4{a^2}b-4a{b^2}}}{{a + b}}} \right)\,{\left( {\dfrac{a}{{a + b}}-\dfrac{b}{{b-a}}-\dfrac{{2a{b^{}}}}{{{a^2}-{b^2}}}} \right)^{-1}} = \)

\( = \left( {\left( {a-b} \right)\left( {a + b} \right)-\dfrac{{4ab\left( {a-b} \right)}}{{a + b}}} \right) \cdot {\left( {\dfrac{a}{{a + b}} + \dfrac{b}{{a-b}}-\dfrac{{2ab}}{{\left( {a-b} \right)\left( {a + b} \right)}}} \right)^{-1}} = \)

\( = \left( {a-b} \right) \cdot \dfrac{{{a^2} + 2ab + {b^2}-4ab}}{{a + b}} \cdot {\left( {\dfrac{{{a^2}-ab + ab + {b^2}-2ab}}{{\left( {a + b} \right)\left( {a-b} \right)}}} \right)^{-1}} = \)

\( = \dfrac{{\left( {a-b} \right)\left( {{a^2}-2ab + {b^2}} \right)}}{{a + b}} \cdot \dfrac{{\left( {a + b} \right)\left( {a-b} \right)}}{{{a^2}-2ab + {b^2}}} = {\left( {a-b} \right)^2}.\)

Ответ:  \({\left( {a-b} \right)^2}.\)