The partial fraction decomposition of 8x29\displaystyle {\frac{{{8}}}{{{x}^{{2}}-{9}}}} can be written in the form of f(x)x3+g(x)x+3,\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{x}-{3}}}}+{\frac{{{g{{\left({x}\right)}}}}}{{{x}+{3}}}}, where

f(x)=\displaystyle {f{{\left({x}\right)}}}=   ,
g(x)=\displaystyle {g{{\left({x}\right)}}}=   .