Partial fractions decomposition of ${\frac{2x}{(x+2)^2}}$ Express in partial fraction form: $\displaystyle{\frac{2x}{(x+2)^2}}$
I think is $\displaystyle{\frac{2x}{(x+2)^{2}} = \frac{A}{x+2}+\frac{B}{(x+2)^2}}$
However when identifying $A$ and $B$, I'm not sure how to calculate A.
E.g.  $$2x = A\cdot (x+2) + B$$
Substitute $x=-2$    
$2\cdot(-2)$ = $A\cdot (2-2) +B$
$-4 = B$
In other questions there is always another factor to multiply by at this stage.

If you go on to rewrite $2x=A(x+2)+B$ as $2x=Ax+(2A+B)$, then you can match up the coefficients of the polynomials (of $x$) on each side.  You must have
$$2=A\qquad\text{and}\qquad 0=2A+B$$
Now solve for $A$ and $B$.  The first equation (obviously!) says $A=2$. When you plug this into the second, obtaining $0=2\cdot2+B$, you get $B=-4$.
Incidentally, where you write "$2x={A\over x+2}+{B\over(x+2)^2}$," the left hand side of the equation should be $2x\over(x+2)^2$, not just $2x$.
