Question

Помогите упростить .

Answer 1

$frac{4}{a-b} + frac{9}{a+b} - frac{8a}{a^2-b^2} = frac{4(a+b)+9(a-b)-8a}{a^2-b^2}=frac{5a-5b}{a^2-b^2}=frac{5(a-b)}{(a-b)(a+b)}=frac{5}{a+b}$

$frac{1}{(x+3)^2}: frac{x}{x^2-9} - frac{x-9}{x^2-9}= frac{(x-3)(x+3)}{x(x+3)^2}- frac{x-9}{x^2-9}= frac{x-3}{x(x+3)}- frac{x-9}{(x-3)(x+3)}= \ =frac{(x-3)^2-x(x-9)}{x(x+3)}=frac{3x+9}{x(x+3)}=frac{3(x+3)}{x(x+3)}=frac{3}{x}$

$frac{b^2}{a^2-2ab} : (frac{2ab}{a^2-4b^2}- frac{b}{a+2b} )= frac{b^2}{a^2-2ab} : frac{2ab-b(a-2b)}{a^2-4b^2}= frac{b^2}{a^2-2ab} : frac{2ab-ab+2b^2}{a^2-4b^2}= \ frac{b^2(a-2b)(a+2b)}{a(a-2b)b(a+2b)}= frac{b}{a}$