Question

Упростить выражение.Очень надо.​

Answer 1

Ответ:

Объяснение:

(b^(1/3)/(b-1) +b/(b^(4/3)-b^(2/3)))·(b^(1/3)-1)·(b-1)/b^(1/3)=(b+b^(2/3)-2)/(b^(1/3)+1)

Решаем по действиям. Начнем со 2-й дроби:

b/(b^(4/3)-b^(2/3))=b^(3/3)/(b^(2/3)·(b^(2/3)-1))=b^(1/3)/(b^(2/3)-1)

Складываем 1-ю и 2-ю дроби:

b^(1/3)/(b-1) +b^(1/3)/(b^(2/3)-1)=(b^(1/3)·(b^(2/3)-1)+b^(1/3)·(b-1))/((b-1)(b^(2/3)-1))=b^(1/3)·(b^(2/3)-1+b-1)/((b-1)(b^(2/3)-1))=b^(1/3)·(b+b^(2/3)-2)/((b-1)(b^(2/3)-1))

Полученный вид выражения:

b^(1/3)·(b+b^(2/3)-2)/((b-1)(b^(2/3)-1)) ·(b^(1/3)-1)·(b-1)/b^(1/3)=(b+b^(2/3)-2)/(b^(2/3)-1) ·(b^(1/3)-1)=(b+b^(2/3)-2)/((b^(1/3)-1)(b^(1/3)+1)) ·(b^(1/3)-1)=(b+b^(2/3)-2)/(b^(1/3)+1)