Question 48570
[a^2-b^2 \ a^2-3ab-2b^2]/[a^2-4ab+4b^2 \ a-2b ]

Factor where you can as follows:

[(a-b)(a+b)/(a^2-3ab-2b^2)]/[(a-2b)(a-2b)/(a-2b)]

Cancel where you can to get:

[(a-b)(a+b)/a^2-3ab-2b^2]/(a-2b)

This is as far as you can go.

Comment: I think you may have made a typo in posting a^2-3ab-2b^2.
It probably should be a^2-3ab+2b^2.  That would factor into 
(a-2b)(a-b) and would result in a lot more canceling.

Cheers,
Stan H.