2 x^2+1 x^3-1 = A x-1 + B x+C x^2+x+1 7 A+2 B+C=

Step-by-step solution

Here, 2 x^2+1 x^3-1 = A x-1 + B x+C x^2+x+1 Resolving into partial fractions, 2 x^2+1 x^3-1 = A (x^2+x+1 )+(B x+C)(x-1) (x-1) (x^2+x+1 ) aligned & 2 x^2+1=A x^2+A x+A+B x^2-B x+C x-C & 2 x^2+1=x^2(A+B)+x(A-B+C)+A-C aligned Comparing with coefficient, we get A+B=2, A-B+C=0 and A-C=1 Clearly, A=1, B=1 and C=0 So, 7 A+2 B+C=7( l )+2( l )+0=9