Question

упростите выражение .

Answer 1

$( frac{a-3b}{a^2+3ab} - frac{a+3b}{a^2-3ab} ): frac{4b^2}{9b^2-a^2}= ( frac{a-3b}{a(a+3b)} - frac{a+3b}{a(a-3b)} )* frac{9b^2-a^2}{4b^2}= \ \ frac{(a-3b)^2-(a+3b)^2}{a(a+3b)(a-3b)}* frac{(3b-a)(3b+a)}{4b^2}= frac{a^2-6ab+9b^2-(a^2+6ab+9b^2)}{a(a-3b)}* frac{(3b-a)}{4b^2}= \ \ frac{a^2-6ab+9b^2-a^2-6ab-9b^2}{a(a-3b)}* frac{(3b-a)}{4b^2}= frac{-12ab}{a(a-3b)}* frac{-(a-3b)}{4b^2}= frac{12b}{4b^2} = frac{3}{b}$