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

Step-by-step solution

3 x+2 (x+1) (2 x^2+3 ) = A x+1 + B x+C 2 x^2+3 3 x+2=A (2 x^2+3 )+(B x+C)(x+1) On putting x+1=03(-1)+2=A [2(-1)^2+3 ] -3+2=A(5) A=- 1 5 Now on comparing the coefficients of like power of x Coefficient of x^20=2 A+B B= 2 5 and coefficient of x3=B+C C=3- 2 5 = 13 5 A+C-B=- 1 5 + 13 5 - 2 5 = 13-2-1 5 = 10 5 =2