Question

Упростите выражение:
1) $( frac{a^2}{a+b} - frac{a^3}{a^2+2ab+b^2} ) : (frac{a}{a+b} - frac{a^2}{a^2-b^2} )$

Answer 1

$1)dfrac{a^2}{a+b}- dfrac{a^3}{a^2+2ab+b^2}=dfrac{a^2(a+b)-a^3}{(a+b)^2}= dfrac{a^3+a^2b-a^3}{(a+b)^2}= dfrac{a^2b}{(a+b)^2}\2) dfrac{a}{a+b}- dfrac{a^2}{a^2-b^2}= dfrac{a(a-b)-a^2}{(a-b)(a+b)}= dfrac{a^2-ab-a^2}{(a-b)(a+b)}=-dfrac{ab}{(a-b)(a+b)}\3) dfrac{a^2b}{(a+b)^2}:(-dfrac{ab}{(a-b)(a+b)})= dfrac{-a(a-b)}{a+b}=dfrac{ab-a^2}{a+b}$