The partial fraction decomposition of x21x23x4\displaystyle \frac{{-{x}-{21}}}{{{x}^{{2}}-{3}{x}-{4}}} can be written in the form of f(x)x4+g(x)x+1,\displaystyle \frac{{{f{{\left({x}\right)}}}}}{{{x}-{4}}}+\frac{{{g{{\left({x}\right)}}}}}{{{x}+{1}}}, where

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