⇒3x+1=A(x2+2)+(Bx+C)(x−1) ⇒3x+1=(A+B)x2+(C−B)x+(2A−C) Comparing both sides, we get A+B=0 ⇒A=−B⋅⋅⋅⋅⋅⋅⋅(i) and C−B=3⋅⋅⋅⋅⋅⋅⋅(ii) and 2A−C=1⋅⋅⋅⋅⋅⋅⋅(iii) put the value of A from Eq. (i) to Eq. (iii) ⇒−2B−C=1 ⇒C=−2B−1⋅⋅⋅⋅⋅⋅⋅(iv) By Eqs. (ii) and (iv), We get (−2B−1)−B=3⇒B=−4∕3 and A=−(−4∕3)=4∕3 Also, C=−2B−1=−2(−4∕3)−1 =
