simplification of multiplying rational expressions

Question

I cant' get the right answer to simplifying this expression:

$$\frac{x^2+x-6}{x} \cdot \frac{x^2-3x}{x^2-9}$$

The answer I have is ${x - 2}.$

I can simplify it to

$$\frac{x^2-6}{x} \cdot \frac{x(x-3)}{(x-3)(x+3)}$$

And from there to

$$(x - 6) \cdot \frac{x}{x+3}$$

I'm not sure if I've taken a wrong turn or how ${x - 2}$ was obtained from here.

Answer 1

It was probably just misread: $$ \frac{(x-2)(x+3)}{x}\frac{x(x-3)}{(x-3)(x+3)} = \frac{x-2}{x}\frac{x(x-3)}{(x-3)}=x-2 $$

Answer 2

HINT:

In the first line

$$x^2+x-6=(x+3)(x-2)$$

Answer 3

You must have misread x² +x - 6 as x² - 6

we can simplify this to (x+3)(x-2)