I need to find constants A and B that work.

Rewrite the R side to the common denominator (x)(x-1)

{A(x-1) + B (x) ] / (x(x-1) now equate the numerators from both sides

A(x-1) + B (x) = x+3

Ax -A + Bx = x+3

Obviously A = -3

then

-3x + Bx = x so B = 4