Partial Fractions Decomposition I am failing to understand partial fraction decomposition in cases like the following:
Provide the partial fraction decomposition of the following:
$$\frac{x+2}{(x-4)^3(x^2 + 4x + 16)}$$
I see this and I think of 
$$\frac{A}{x-4} + \frac{Bx+C}{(x-4)^2} + \frac{Dx^2 + Ex + F}{(x-4)^3} + \frac{Gx+H}{x^2 + 4x + 16}$$
But I am told that the correct answer is
$$\frac{A}{x-4} + \frac{B}{(x-4)^2} + \frac{C}{(x-4)^3} + \frac{Dx+E}{x^2 + 4x + 16}$$
What exactly is the numerator of each fraction based on?

You may see the redundancy of the $Bx$ term as follows:
\begin{align}
\frac{Bx + C}{(x - 4)^2}
& = \frac{Bx}{(x - 4)^2} + \frac{C}{(x - 4)^2} \\
& = \frac{B(x - 4)}{(x - 4)^2} + \frac{4B}{(x - 4)^2} + \frac{C}{(x - 4)^2}\\
& = \frac{B}{x - 4} + \frac{4B + C}{(x - 4)^2}.
\end{align}
