Answer
option (ii) is correct.
Work Step by Step
we have $r(x)=\dfrac{2x+8}{(x-1)(x^2+4)}$
Here, $x^2+4$ can not be factorized so the decomposion will have linear function of $x$.
This shows a one single root and one repeated root.
Applying the partial fraction decomposition rule.
Therefore,
$\dfrac{2x+8}{(x-1)(x^2+4)}=\dfrac{A}{x-1}+\dfrac{Bx+C}{x^2+4}$
Hence, option (ii) is correct.