The partial fraction decomposition of $\displaystyle \frac{x^2+6}{(x-3)(x^2+4)}$ can be written in the form of $\displaystyle \frac{f(x)}{x-3} +\frac{g(x)}{x^2+4}.$
The possible anwsers for $f(x)$ and $g(x)$ are (a) $A$, a constant, or (b) $Ax+B$, a linear function.
$f(x)$ is in the form of (input a or b)
and $g(x)$ is in the form of (input a or b) .