Okay so I've been sitting with this for a while and I need some help.

36a^2-12a+1 / 1-36a

= (simplified)

(6a-1)(6a-1) / (1+6a)(1-6a)

= (simplified again)

(6a-1)(6a-1) / (-1) * (6a + 1)(6a - 1)

= (ye again)

- (6a - 1) / (6a + 1)

Mr F says: This is correct. And if you take the minus back in to the top you get (-6a + 1)/(6a + 1) = (1 - 6a)/(6a + 1). All these answers are equivalent and it's a matter of choice which one is used. And obviously your book makes a choice in what it gives as its answer.
^ see that little minus over there? It's not supposed to be there and I dont understand where it has gone to. Could someone explain why the answer is not negative ALL THE TIME when I use the (-1) * xxxx method?

Also now I see that the answer is supposed to be the other way = (1-6a) / 1+6a).. what says that I can't do as I first did? Somehow it does not seem wrong to me.. please someone explain this to me!