\[\left( a - b + \frac{4ab}{a - b} \right)\left( \frac{4a^{2}}{a^{2} + 2ab + b^{2}} - \frac{2a}{a + b} \right) =\]
\[= 2a\]
\[1)\ (a - b)^{\backslash a - b} + \frac{4ab}{a - b} =\]
\[= \frac{a^{2} - 2ab + b^{2} + 4ab}{a - b} = \frac{a^{2} + 2ab + b^{2}}{a - b} =\]
\[= \frac{(a + b)^{2}}{a - b}\ \]
\[2)\ \frac{4a^{2}}{a^{2} + 2ab + b^{2}} - \frac{2a}{a + b} = \frac{4a^{2}}{(a + b)^{2}} -\]
\[- \frac{2a^{\backslash a + b}}{a + b} = \frac{4a^{2} - 2a^{2} - 2ab}{(a + b)^{2}} = \frac{2a^{2} - 2ab}{(a + b)^{2}} =\]
\[= \frac{2a(a - b)}{(a + b)^{2}}\]
\[3)\ \ \frac{(a + b)^{2}}{a - b} \cdot \frac{2a(a - b)}{(a + b)^{2}} = 2a\]