When the degree of the numerator is the same or greater than
the degree of the denominator the expression must first be 
divided out by long division:


                 4
x²+4x+4)4x²+11x+ 0
        4x²+16x+16
            -5x-16

 = 4 + 

Next we find the partial fraction
decomposition of  and when we finish
we will add it to the 4:

 

Factor the denominator as (x+2)(x+2) or (x+2)².

 

That is a power in the denominator, so we must include in the 
decomposition factors with denominators of it and all lower 
powers, so we assume A and B such that:

  =  + 

Clear of fractions by multiplying through by
the LCD (x+2)²:

-5x - 16 = A + B(x + 2)
-5x - 16 = A + Bx + 2B

Equate the coefficients of x

-5 = B

Equate the constants:

-16 = A + 2B

Substitute -5 for B

-16 = A + 2(-5)
-16 = A - 10
 -6 = A

So

  =  + 

And therefore the original:

 = 4 +  = 4 +  + 

or a bit simpler:

4 -  - 

Edwin