If x (1+x^2 )(3-2 x) = B x+C 1+x^2 + A 3-2 x , then C is

Step-by-step solution

We have, aligned & x (1+x^2 )(3-2 x) = B x+C 1+x^2 + A (3-2 x) & x (1+x^2 )(3-2 x) = B x(3-2 x)+C(3-2 x)+A (1+x^2 ) (1+x^2 )(3-2 x) & x=B x(3-2 x)+C(3-2 x)+A (1+x^2 ) & x=3 B x-2 B x^2+3 C-2 C x+A+A x^2 & =x=(A-2 B) x^2+(3 B-2 C) x+A+3 C aligned Equating the coefficient of x^2, x and constant term A-2 B=0,3 B-2 C=1, A+3 C=0 Solving, we get aligned & A & = 6 13 , B= 3 13 , C=- 2 13 & C & =- 2 13 aligned