Question

If $\frac{x^{4} + 24 x^{2} + 28}{\left(x^{2} + 1\right)^{3}} = \frac{A }{\left(x^{2} + 1\right)} + \frac{B}{\left(x^{2} + 1\right)^{2}} + \frac{C}{\left(x^{2} + 1\right)^{3}}$ then $A + C =$

• A. 12
• B. 10
• C. 9
• D. 6

Answer 1

Answer: (D)

6

Answer 2

If $\frac{x^{4}+24 x^{2}+28}{\left(x^{2}+1\right)^{3}}=\frac{A}{x^{2}+1}+\frac{B}{\left(x^{2}+1\right)^{2}}$
$+\frac{C}{\left(x^{2}+1\right)^{3}}$
$\Rightarrow x^{4}+24 x^{2}+28=A\left(x^{2}+1\right)^{2}+B\left(x^{2}+1\right)+C$
On comparing the coefficient of different terms
$A=1;\, 2 A+B=24$ and $A+B+C=28$
$\Rightarrow A=1,\, B=22$, so $A+C=6$