⇒2x+1=A(x−1)(x2+1)+B(x2+1) +(Cx+D)(x−1)2 ⇒2x+1=x3(A+C)+x2(−A+B−2C+D) +x(A+C−2D)+(−A+B+D) On comparing coefficients of x3,x2,x and constant terms both sides we get. A+C=0 . . . (i) −A+B−2C+D=0 . . . (ii) A+C−2D=2 . . . (iii) and −A+B+D=1 . . . (iv) On solving Eqs. (i), (ii), (iii) and (iv), we get A=