When I try to decompose: (x + 1) / ((x + 2)^2)
I end up with: x + 1 = A(x + 2)^2 + B(x + 2)
How? Kindly please reply with your steps. Thank you.
And grouping to begin seeing correspondence of the numerators,
Now, carefully equate the corresponding parts of the numerator:
because you are comparing x+1 with Ax+2A+B
The coefficient on x is 1, so A=1.
Using this for A in the constants relationship, 2*1+B=1 means B=-1