I need to take the derivative of... (-x^2 - 2x) / (x^2 + 2x + 2)^2

I know I use the quotient rule which is

(x^2 + 2 x + 2)^2 (-2x - 2) - (-x^2 - 2x) 2(x^2 + 2)

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(x^2 + 2x + 2)^4

I am having trouble simplifying this and getting to the correct answer. Can someone please show me how to do this!