Question

(2ab/4a^2-9b^2-b/2a-3b):(1-2a-3b/2a+3b)

Answer 1

$( frac{2ab}{4a^2-9b^2}- frac{b}{2a-3b}):(1- frac{2a-3b}{2a+3b})= \ \ =( frac{2ab}{(2a-3b)(2a+3b)}- frac{b(2a+3b)}{(2a-3b)(2a+3b)}):( frac{2a+3b}{2a+3b} - frac{2a-3b}{2a+3b})= \ \ =frac{2ab-b(2a+3b)}{(2a-3b)(2a+3b)}:( frac{2a+3b-2a+3b}{2a+3b})= \ \ =frac{2ab-2ab-3b^2)}{(2a-3b)(2a+3b)}:( frac{6b}{2a+3b})=frac{(2ab-2ab-3b^2)}{(2a-3b)(2a+3b)}cdot frac{2a+3b}{6b}= frac{-b}{2cdot(2a-3b)}$