The answer given by the book:

When factoring the denominators I got the following: (3a + 6)(a + 2)b, (2b - 2)(2b - 2)a, (a + 2)b^3 edit: whoops, I wrote the 6 as a b the first time.

I found the different factors with the highest powers to be: (3a + b)(a + 2)(2b - 2)(a)(b^3)

I don't understand how to get from the last step I performed to the answer given in the book. I suspect I'm doing something wrong. Any help would be greatly appreciated. Thank you.