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

Step-by-step solution

Given, 3 x+1 (x-1)(x+3) = A x-1 + B x+3 aligned & 3 x +1= A ( x +3)+ B ( x -1) & 3 x +1=( A + B ) x +(3 ~A - B ) aligned On equating the coefficient of x from both sides, we get and array rr A + B & =3 3 ~A - B & =1 array On adding Eqs. (i) and (ii), we get 4 ~A =4 A =1 From Eq. (i), we get aligned B=3-A &=3-1=2 ⁻¹ A B = ⁻¹ ( 1 2 ) &= 6 aligned