Can someone please help me finish this derivative problem?

Here's the problem:

$\displaystyle f(v) = [ (1-2v) / (1+v) ] ^ 3$

Here's my work so far:

f '(v) = 3[ (1-2v) / (1+v)] ^2 times [(1+v)(-2) - (1-2v)(v) / (1+v)^2 ]

f '(v) = [3(1-2v)^2] / (1+v)2 times [-2 - 2v - v + 2v^2] / (1+v)^2 ]

f '(v) = " times (-2-3v+2v^2) / (1+v)^2

f '(v) = [3(1-2v)^2][-2-3v+2v^2] / [1+v]^4

..thats as far as I got, but the answer is: $\displaystyle [ -9(2v - 1)^2 ] / (1+v)^4$

How did they get that??