The partial fraction decomposition of x2+9x3+4x2\displaystyle {\frac{{{x}^{{2}}+{9}}}{{{x}^{{3}}+{4}{x}^{{2}}}}} can be written in the form of f(x)x+g(x)x2+h(x)x+4,\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{x}}}}+{\frac{{{g{{\left({x}\right)}}}}}{{{x}^{{2}}}}}+{\frac{{{h}{\left({x}\right)}}}{{{x}+{4}}}}, where

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

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