Question

выполните действие 1/(x+3)^2:x/x^2-9-x-9/x^2-9

Answer 1

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