How do I simplify this expression about factorization? I am trying to simplify this
$$\frac{9x^2 - x^4}  {x^2 - 6x +9}$$
The solution is 
$$\frac{-x^2(x +3)}{x-3} = \frac{-x^3 - 3x^2}{x-3} $$
I have done $$\frac{x^2(9-x^2)}{(x-3)(x-3)} = \frac{x^2(3-x)(3+x)}{(x-3)(x-3)} $$
but I do not find a way to simplify 
How can I simplify to get the answer?
I have to use
$${(a +b)(a -b)} = {a^2 - b^2} $$
$${(a +b)^2} = {a^2 + 2ab+b^2} $$
$${(a -b)^2} = {a^2 - 2ab+b^2} $$

Observe that
$$
9x^2-x^4=-x^2(x^2-9)=-x^2(x-3)(x+3).
$$
Thus, we have that
$$
\frac{9x^2-x^4}{x^2-6x+9}=\frac{-x^2(x-3)(x+3)}{(x-3)^2}=-x^2\left(\frac{x+3}{x-3}\right).
$$ 
