How do I simplify this expression about factorization?

Question

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

$${(a +b)(a -b)} = {a^2 - b^2} $$ $${(a +b)^2} = {a^2 + 2ab+b^2} $$ $${(a -b)^2} = {a^2 - 2ab+b^2} $$

Answer 1

Notice that $(3-x)=-(x-3)$. Simplify accordingly.

Answer 2

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