how to write the partial fraction of a rational expression

Question

what is the partial fraction decomposition of x+1 divided by x^2(x-2)^2.

Answer 1

 

Equating the coefficients  of variables and constants.

Divide to each side by 4.

Substitute the B value in 4A-4B = 1

Substitute the A value in A+C = 0

Substitute the A,B,C values in -4A+B-2C+D = 0

Partial decomposition is