The partial fraction decomposition of 6x2+11x−19(x+2)(x2−2x+9)\displaystyle \frac{{{6}{x}^{{2}}+{11}{x}-{19}}}{{{\left({x}+{2}\right)}{\left({x}^{{2}}-{2}{x}+{9}\right)}}} can be written in the form of f(x)(x+2)+g(x)(x2−2x+9),\displaystyle \frac{{{f{{\left({x}\right)}}}}}{{{\left({x}+{2}\right)}}}+\frac{{{g{{\left({x}\right)}}}}}{{{\left({x}^{{2}}-{2}{x}+{9}\right)}}}, where
f(x)=\displaystyle {f{{\left({x}\right)}}}=   ,
g(x)=\displaystyle {g{{\left({x}\right)}}}=   .

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