Partial fraction with a constant as numerator I am trying to express this as partial fraction:
$$\frac{1}{(x+1)(x^2+2x+2)}$$
I have a similar exaple that has $5x$ as numerator, it is easy to understand. I do not know what to do with 1 in the numerator, how to solve it?!

You want to find $A, B,$ and $C$ such that
$$\frac{1}{(x+1)(x^2 + 2x + 2)} = \frac{A}{x+1} + \frac{Bx + C}{x^2 + 2x + 2}
$$
That is such that
$$\begin{align}0x^2 + 0x + 1 &= A(x^2 + 2x + 2) + (x+1)(Bx+c)\\
&= (A+B)x^2 + (2A+B+C)x + 2A + C.
\end{align}$$
So you get three equations
$$\begin{align} 0 &= A + B \\ 
0 &= 2A + B + C \\
1 &= 2A + C.
\end{align}$$
Solving this I get $A =1, B = -1, C= -1$.
