Question

((a - b)/(a ^ 2 + ab) - a/(ab + b ^ 2)) / ((b ^ 2)/(a ^ 3 - a * b ^ 2) + 1/(a + b))

Answer 1

Ответ:

$\displaystyle -\frac{a-b}{b}$

Объяснение:

$\displaystyle \left(\frac{a-b}{a(a+b)}-\frac{a}{b(a+b)}\right):\left(\frac{b^2}{a(a^2-b^2)}+\frac{1}{a+b}\right)=\\\\\\\left(\frac{b(a-b)}{ab(a+b)}-\frac{a^2}{ab(a+b)}\right):\left(\frac{b^2}{a(a-b)(a+b)}+\frac{1}{a+b}\right)=\\\\\\\frac{b(a-b)-a^2}{ab(a+b)}:\left(\frac{b^2}{a(a-b)(a+b)}+\frac{a(a-b)}{a(a-b)(a+b)}\right)=$

$\displaystyle \frac{ab-b^2-a^2}{ab(a+b)}:\left(\frac{b^2+a(a-b)}{a(a-b)(a+b)}\right)=\\\\\\\frac{ab-b^2-a^2}{ab(a+b)}:\frac{b^2+a^2-ab}{a(a-b)(a+b)}=\\\\\\\frac{-(-ab+b^2+a^2)}{ab(a+b)}\cdot \frac{a(a-b)(a+b)}{b^2+a^2-ab}\\\\\\\frac{-1}{b}\cdot \frac{a-b}{1}=-\frac{a-b}{b}$