Question

докажите тождество даю 44 балла

Answer 1

$dfrac{b}{b-a}+ dfrac{a^2-b^2}{ab+a^2} * dfrac{b^2}{(b-a)^2} = \ \ = dfrac{b}{b-a}- dfrac{b^2-a^2}{a(a+b)} * dfrac{b^2}{(b-a)^2}= \ \ = dfrac{b}{b-a}- dfrac{(b-a)(b+a)}{a(a+b)}* dfrac{b^2}{(b-a)^2}= \ \ = dfrac{b}{b-a}- dfrac{b^2}{a(b-a)}= \ \ = dfrac{ab-b^2}{a(b-a)}= \ \ =- dfrac{b^2-ab}{a(b-a)}= \ \ =- dfrac{b(b-a)}{a(b-a)}= \ \ =- dfrac{b}{a}$