Question

разложите на множители:$frac{1}{(x+3)^{2}} : frac{x}{ x^{2}-9 } - frac{x-9}{ x^{2-9} }$

Answer 1

$frac{1}{(x+3)^2}*frac{x^2-9}{x}=frac{(x-3)(x+3)}{x(x+3)^2}=frac{x-3}{x(x+3)}\ frac{x-3}{x(x+3)}-frac{x-9}{x^2-9}=frac{x-3}{x(x+3)}-frac{x-9}{(x+3)(x-3)}=frac{(x-3)^2-x(x-9)}{x(x^2-9)}=frac{x^2-6x+9-x^2+9x}{x(x^2-9)}=frac{3(x+3)}{x(x-3)(x+3)}=frac{3}{x(x-3)}$