Quotient rule?

Asked to differentiate this function:

Used quotient rule but I don't know why the answer I've got which is right is different to how the answer is given, don't know what method they have used?
The answer given is like this:

Then simplified to:

Please can someone explain to me how they have split it into two fractions and how it is simplified? I know it's really easy but my mind is just not working well right now.
Thanks!

they are using this law: (a + b)/c = a/c + b/c
And then they simplify which is why the "c" in the answer is different in both parts

Thanks! Now I understand the first part but I still don't get the final answer.

hahha I kno...I was lookin at it just now..and I'm just as stuck as u atm. I know they put them back together and multiply out a part of it..but...still cant manipulate it round to give me that answer

hahha I kno...I was lookin at it just now..and I'm just as stuck as u atm. I know they put them back together and multiply out a part of it..but...still cant manipulate it round to give me that answer

got it..yeh..you just have to get common factor (1 +x^2)^5 and then factorize and multiply out "the" bracket and then you get 12x(1+x^2)^5*(1-x) as ur numerator