When I try to decompose: (x + 1) / ((x + 2)^2)

I end up with: x + 1 = A(x + 2)^2 + B(x + 2)

this ends up with A = 1/2, B = - 1/2, so the answer seemingly should be:

1/2(x + 2) - 1/2(x + 2)^2

This doesn't make sense however as the result when these terms are added back is

(x + 1) /

**2**(x + 2)^2 rather than (x + 1) / (x + 2)^2

Can someone explain the result to me\

Thanks