Note that a/(x-b) + b = a/(x - b) + b(x-b)/(x-b) = (a + b(x - b)) / (x - b). Then (a + bx - b^2) / (x - b).

Cross multiply.

(1 - 2x)(x - b) = (3x - 2)(a + bx - b^2)

x - b - 2x^2 + 2bx = 3ax + 3bx^2 - 3b^2 x + 2b^2 - 2a - 2bx

-2x^2 + (2b + 1)x - b = 3bx^2 + (3a - 3b^2 - 2b)x + 2b^2 - 2a

Equate coefficients

(*) -2 = 3b

(**) 2b + 1 = 3a - 3b^2 - 2b

(***) 2b^2 - 2a = -b

(*) => b = -2/3. Plug this into (**) and (***).

(**) => 2(-2/3) + 1 = 3a - 3(-2/3)^2 - 2(-2/3)

=> -4/3 + 1 = 3a - 3(4/9) + 4/3

=> -1/3 = 3a - 4/3 + 4/3

=> -1/3 = 3a

=> a = -1/9

(***) => 2(-2/3)^2 - 2a = -(-2/3)

=> 2(4/9) - 2a = 4/3

=> 8/9 - 2a = 12/9

=> -2a = 12/9 - 8/9

=> -2a = 4/9

=> a = -2/9

We see that a = -1/9 and a = -2/9 which is impossible. There must be some typo.