Hint: x^2 - 2x - 3 = (x-3)(x+1), x^2 - x - 6 = (x-3)(x+2), x^2 + 2x = x(x+2), and x^2 - 4x = x(x-4).
Try double checking your calculations with the above results.
Your major mistake is the way you go about factoring the second term. Instead of using the times sign x I'm just going to write it like this:
It's the same thing. You factored it all wrong, can you see where the factoring went wrong?
Just re-factor these one-by-one,
Edit: I 'd like to add that all of the errors you make (that (I've seen so far) are just factoring quadratic expressions, so you should review that. You seem to know how to approach rational expressions like this methodologically (factoring, cancelling, and simplifying,) but you're hung-up on the factoring bit.