Partial fraction $\frac{x}{(1+x)^2}$ How do you compute $\dfrac{x}{(1+x)^2}$ using partial fractions? The reason I ask is because when I try to solve it I keep getting an impossible $A, B$.
$A(1+x) + B(1+x) = x$
$A + Ax + B + Bx = x$
$(A+B)x = 1$
$(A+B) = 0$
However a practice problem I'm working on implies this can be solved by partial fractions, but doesn't go into detail. 

$$\frac{x}{(1 + x)^2} = \frac{A}{1 + x} + \frac{B}{(1 + x)^2}$$
$$x=A(1+x)+B $$
put $x=-1$ gives $B=-1$
and compare coefficient of x from both side gives $A=1$
so answer is $$\frac{x}{(1 + x)^2} = \frac{1}{1 + x} - \frac{1}{(1 + x)^2}$$
