If the equivalent partial fraction of x^3 (2 x-1)(x+2)(x-3) is of the form A+ B 2 x-1 + C x+2 + D x-3 then the value of A+B+C=

Step-by-step solution

x^3 (2 x-1)(x+2)(x-3) =A+ B (2 x-1) + C (x+2) + D (x-3) aligned & x^3=A(2 x-1)(x+2)(x-3)+ B (x+2)(x-3)+ C & (2 x-1)(x-3)+ D (2 x-1)(x+2) ( i ) aligned Put x=1 / 2 1 8 =B ( 1 2 +2 ) ( 1 2 -3 ) B= -1 50 Put x=-28=C(-4-1)(-2-3) C=8 / 25 Put x=39=D(6-1)(3+2) D=9 / 25 Comparing coefficient of x^3 both sides in (i) 1=2 ~A A =1 / 2A+B+C= 1 2 - 1 50 + 8 25 = 25-1-16 50 = 8 50 = 4 25