Answer:
Option D
Explanation:
We have,
$\frac{2x+7}{(x^{2}+4)(x^{2}+9)(x^{2}+16)}= \frac{Ax+1}{x^{2}+4}+\frac{Bx+m}{x^{2}+9}+\frac{Cx+n}{x^{2}+16}$
$ 2x+7= (Ax+l)(x^{2}+9)(x^{2}+16) +(Bx+m)(x^{2}+4)$
$(x^{2}+16)+(Cx+n)(x^{2}+4)(x^{2}+9)$
put x=2i
4i+7=120Ai+60l $ \Rightarrow \frac{1}{A} =\frac{60}{2}$
put x=3i
6(i) +7 =-105 Bi-35m $\Rightarrow \frac{1}{B}=\frac{-35}{2}$
pit x=4i
8i+7=336 Ci+84n
$\Rightarrow$ $\frac{1}{C} = \frac{84}{2}$
$\therefore$ $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}$= $\frac{60-35+84}{2}= \frac{109}{2}$
