4. Упростить выражение: a²+b² A)(\frac{a²+b²}{ab} - 1) \cdot \frac{2ab}{a-b} 2ab a²-b² Б) (a-b+ \frac{2ab}{a-b}) \cdot \frac{a²-b²}{a²+b²} 1 n m B)( \frac{1}{m-n} - \frac{n}{m²-mn} ): \frac{m}{n-m}.

А) \[\left(\frac{a^2 + b^2}{ab} - 1\right) \cdot \frac{2ab}{a-b}\] \[= \left(\frac{a^2 + b^2 - ab}{ab}\right) \cdot \frac{2ab}{a-b}\] \[= \frac{(a^2 + b^2 - ab) \cdot 2ab}{ab \cdot (a-b)}\] \[= \frac{2(a^2 + b^2 - ab)}{a-b}\] Б) \[\left(a - b + \frac{2ab}{a-b}\right) \cdot \frac{a^2 - b^2}{a^2 + b^2}\] \[= \left(\frac{(a-b)^2 + 2ab}{a-b}\right) \cdot \frac{a^2 - b^2}{a^2 + b^2}\] \[= \left(\frac{a^2 - 2ab + b^2 + 2ab}{a-b}\right) \cdot \frac{(a-b)(a+b)}{a^2 + b^2}\] \[= \frac{a^2 + b^2}{a-b} \cdot \frac{(a-b)(a+b)}{a^2 + b^2}\] \[= a + b\] В) \[\left(\frac{1}{m-n} - \frac{n}{m^2 - mn}\right) : \frac{m}{n-m}\] \[= \left(\frac{1}{m-n} - \frac{n}{m(m - n)}\right) : \frac{m}{n-m}\] \[= \left(\frac{m - n}{m(m - n)}\right) : \frac{m}{n-m}\] \[= \frac{1}{m} : \frac{m}{n-m}\] \[= \frac{1}{m} \cdot \frac{n-m}{m}\] \[= \frac{n-m}{m^2}\]