(8ab)/(a+8b)*((a)/(8b)-(8b)/(a)) при a=8sqrt(3)+7, b=sqrt(3)-3

Разбираемся:

(8ab) / (a + 8b) * (a / (8b) - (8b) / a) = (8ab) / (a + 8b) * (a² - (8b)²) / (8ab) = (a² - (8b)²) / (a + 8b) = (a - 8b)(a + 8b) / (a + 8b) = a - 8b

При a = 8√3 + 7, b = √3 - 3:

8√3 + 7 - 8(√3 - 3) = 8√3 + 7 - 8√3 + 24 = 31

Ответ: 31