(2x-1)/((x-1)^2(x^2+x+1)^3)

2x− 1
(x− 1)2(x2 + x + 1)3
=
A
x− 1
+
B
(x− 1)2
+
Cx + D
x2 + x + 1
+
Ex + F
(x2 + x + 1)2
+
Gx + H
(x2 + x + 1)3
We have to find the value of A,B,C,D,E, F,G,H.
Above equation gives:
2x− 1 = A(x− 1)(x2 +x+ 1)3 +B(x2 +x+ 1)3 + (Cx+D)(x2 +x+ 1)2(x− 1)2
+(Ex + F )(x2 + x + 1)(x− 1)2 + (Gx + H)(x− 1)2
Putting x = 1 in above, we...