Question

$\frac{2x+1}{(x-1)(x^2+1)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+1}\Rightarrow C=$

• A. 0
• B. 1/2
• C. -1/2
• D. 5/2

Answer 1

Answer: (B)

1/2

LHS $=\frac{2x+1}{(x-1)(x^2+1)}$; RHS $=\frac{A(x^2+1)+(Bx+c)(x-1)}{(x-1)(x^2+1)}$
LHS=RHS
$2x+1=A(x^2+1)+(Bx+c)(x-1)$----------(1)
Checking the co-efficient of $x^2$ in LHS & RHS
As we get $A+B=0$------------(2)
Co-efficient of$x-B+C=2$ -----------(3)
Co-efficient of $11=A-C$----------------(4)
$A=-B$ from (1) keep in (4) we get $B+C=-1$ -------------(5)
$-B+C=2$ from (3)
from (5) and (3) we get
$C=1/2$