The partial fraction decomposition of 6(x1)(x+1)\displaystyle {\frac{{{6}}}{{{\left({x}-{1}\right)}{\left({x}+{1}\right)}}}} can be written in the form of f(x)x1+g(x)x+1,\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{x}-{1}}}}+{\frac{{{g{{\left({x}\right)}}}}}{{{x}+{1}}}}, where
f(x)=\displaystyle {f{{\left({x}\right)}}}=   ,
g(x)=\displaystyle {g{{\left({x}\right)}}}=   .