If d d x ( x^2 (x+2)(2 x+3) )= A (x+2)^2 + B (2 x+3)^2 then A + B =

Step-by-step solution

d d x ( x^2 (x+2)(2 x+3) )= A (x+2)^2 + B (2 x+3)^2 ( 7 x^2+12 x (x+2)(2 x+3) )= A (x+2)^2 + B (2 x+3)^2 ...(i) The form of the partial fraction decomposition is 7 x^2+12 x (x+2)^2(2 x+3)^2 = A x+2 + B (x+2)^2 + C (2 x+3) + D (2 x+3)^2 ...(ii) array r 7 x^2+12 x= A (x+2)(2 x+3)^2+ B (2 x+3)^2+ C (x+2)^2(2 x+3)+ D (x+2)^2 array aligned & 7 x^2+12 x=x^3(4 ~A +2 C )+x^2(20 ~A +4 ~B +11 C + D )+ & x(33 ~A +12 ~B +20 C +4 D )+18 ~A +9 ~B +12 C +4 D aligned Comparing the coefficients, we get: aligned & 4 A+2 C=0 & 20 A+4