3x+1/x^2+2x-3=A/x-1+B/X+3(3x+1)/(x-1)(x+3)=[A(x+3)+B(x-1)]/(x-1)(x+3)即：3x+1=(A+B)x+(3A-B)即：A+B=3，3A-B=1解之，A=1，B=2
