Question

a^3+8b^3/(a-b)^5 : 4a^2b+16b^3-8ab^2/(b-a)^5

Answer 1

Ответ:

$\displaystyle -\frac{a+2b}{4b}$

Объяснение:

$\displaystyle \frac{a^3+8b^3}{(a-b)^5} :\frac{4a^2b+16b^3-8ab^2}{(b-a)^5}=\\\\\\\frac{(a + 2b)(a^2 - 2ab + 4b^2)}{(a-b)^5} :\frac{4b(a^2 - 2ab + 4b^2)}{-(a-b)^5}=\\\\\\\frac{(a + 2b)(a^2 - 2ab + 4b^2)}{(a-b)^5} \cdot \frac{-(a-b)^5}{4b(a^2 - 2ab + 4b^2)}=\\\\\\\frac{a + 2b}{1} \cdot \frac{-1}{4b}=-\frac{a+2b}{4b}$