Ax+B/(x+1)+C/(x-2)
=Ax(x+1)(x-2)/(x+1)(x-2)+B(x-2)/(x+1)(x-2)+C(x+1)/(x+1)(x-2)
={Ax(x^2-x-2)+Bx-2B+cx+c}/(x+1)(x-2)
Ax(x^2-x-2)+Bx-2B+cx+c=6
Bx-2B+cx+c=6
A=0
B+C=0
C-2B=6
B=-2 C=2
Ax+B/(x+1)+C/(x-2)
=Ax(x+1)(x-2)/(x+1)(x-2)+B(x-2)/(x+1)(x-2)+C(x+1)/(x+1)(x-2)
={Ax(x^2-x-2)+Bx-2B+cx+c}/(x+1)(x-2)
Ax(x^2-x-2)+Bx-2B+cx+c=6
Bx-2B+cx+c=6
A=0
B+C=0
C-2B=6
B=-2 C=2