Hi, can someone please help me understand how this problem is solved?

This is the problem:

This is as far as I get (multiply first fraction by reciprocal of second fraction):

(ignore the red question mark)

I understand the steps and how to divide rational expressions (including this one). I just don't know how I should simplify the numerator in this case.

I know the answer. It is:

=

=

Particularly I don't understand how x^2-6x+15 became (x-5)(x-1). Because, (x-5)(x-1)= x^2-6x-5 and not x^2-6x+15. Can someone please explain how the numerator was simplified?