Question

(a ^ 2 - 4b ^ 2)/(9a ^ 2 - b ^ 2) / ((a ^ 2 + 4ab + 4b ^ 2)/(9a ^ 2 - 6ab + b ^ 2)) * (3a + b)/(a - 2b)

Answer 1

Ответ:

$\frac{ \frac{ \frac{ {a}^{2} - 4 {b}^{2} }{9 {a}^{2} - {b}^{2} } }{ {a}^{2} + 4ab + 4 {b}^{2} } }{9 {a}^{2} - 6ab + {b}^{2} } \times \frac{3a + b}{a - 2b} = \\ = \frac{ \frac{ \frac{(a - 2b)(a + 2b)}{(3a - b)(3a + b)} }{ {(a + 2b)}^{2} } }{ {(3a - b)}^{2} } \times \frac{3a + b}{a - 2b} = \\ = \frac{(a - 2b)( a + 2b)}{(3a - b)(3a + b)} \times \frac{ {(3a - b)}^{2} }{ {(a + 2b)}^{2} } \times \frac{3a + b}{a - 2b} = \\ = \frac{3a - b}{a + 2b}$