The partial fraction decomposition of $\displaystyle {\frac{{{x}^{{2}}+{11}}}{{{\left({x}-{3}\right)}{\left({x}^{{2}}+{4}\right)}}}}$ can be written in the form of $\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{x}-{3}}}}+{\frac{{{g{{\left({x}\right)}}}}}{{{x}^{{2}}+{4}}}}.$
The possible anwsers for $\displaystyle {f{{\left({x}\right)}}}$ and $\displaystyle {g{{\left({x}\right)}}}$ are (a) $\displaystyle {A}$, a constant, or (b) $\displaystyle {A}{x}+{B}$, a linear function.
$\displaystyle {f{{\left({x}\right)}}}$ is in the form of (input a or b)
and $\displaystyle {g{{\left({x}\right)}}}$ is in the form of (input a or b) .