Упростите выражение: ((a+2b)^2/(3(a-4b))-3a)*(a^2-16b^2)/(2a^2-10ab-b^2):(4a+16b)/(27a-21) и найдите его значение при a=1/3; b=-7/3.

\[\left( \frac{(a + 2b)^{2}}{3(a - 4b)} - 3a \right) \cdot \frac{a^{2} - 16b^{2}}{2a^{2} - 10ab - b^{2}}\ \ :\frac{4a + 16b}{27a - 21} =\]

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

\[= \frac{\left( a^{2} + 4ab + 4b^{2} - 9a^{2} + 36ab \right)}{3(a - 4b)} =\]

\[= \frac{\left( - 8a^{2} + 40ab + 4b^{2} \right)}{3(a - 4b)} =\]

\[= \frac{- 4\left( 2a^{2} - 10ab - b^{2} \right)}{3(a - 4b)}\]

\[2)\ \frac{- 4\left( 2a^{2} - 10ab - b^{2} \right)}{3(a - 4b)} \cdot \frac{(a - 4b)(a + 4b)}{2a^{2} - 10ab - b^{2}} =\]

\[= \frac{- 4(a + 4b)}{3}\]

\[3)\ \frac{- 4(a + 4b)}{3} \cdot \frac{27a - 21}{4a + 16b} =\]

\[= \frac{- 4 \cdot 3 \cdot (a + 4b)(9a - 7)}{3 \cdot 4 \cdot (a + 4b)} =\]

\[- (9a - 7) = 7 - 9a;\]

\[a = \frac{1}{3};\ \ b = - \frac{7}{3}:\ \]

\[7 - 9 \cdot \frac{1}{3} = 7 - 3 = 4.\]

\[Ответ:4.\]