If x+1 (2 x-1)(3 x+1) = A 2 x-1 + B 3 x+1 , then 16 A+9 B is equal to

Step-by-step solution

gathered x+1 (2 x-1)(3 x+1) = A 2 x-1 + B 3 x+1 x+1=A(3 x+1)+B(2 x-1) gathered Put, x= 1 2 in Eq. aligned & 3 2 =A (3 1 2 +1 )+B(0) & 3 2 =A 5 2 A= 3 5 aligned Put, aligned & x=- 1 3 in Eq. (i) & 2 3 =A(0)+B (2 (- 1 3 )-1 ) & 2 3 =B (- 5 3 ) B=- 2 5 aligned Consider 16 A+9 B=16 ( 3 5 )+9 (- 2 5 )=6 Hence, option (3) is correct.