Answer:
Option C
Explanation:
We have,
$\frac{x^{2}+5}{(x^{2}+1)(x-2)}=\frac{A}{x-2}+\frac{ Bx+C}{x^{2}+1}$
$\Rightarrow$ $x^{2}+5=A(x^{2}+1)+(Bx+C)(x-2)$
$\Rightarrow$ $x^{2}+5=Ax^{2}+A+Bx^{2}-2Bx+Cx-2C$
Equating the coefficient of x2 ,x and constant terms , we get
1=A+B,0=-2B+C,5=A-2C
solving these equations , we get
$A=\frac{9}{5},B=-\frac{4}{5},C=-\frac{8}{5}$
$\therefore$ A+B+C= $\frac{9-4-8}{5}$
=$\frac{-3}{5}$
