Answer
$$\frac{A}{{x - 1}} + \frac{B}{{{{\left( {x - 1} \right)}^2}}} + \frac{{Cx + D}}{{{x^2} + 1}}$$
Work Step by Step
$$\eqalign{
& \frac{{20x}}{{{{\left( {x - 1} \right)}^2}\left( {{x^2} + 1} \right)}} \cr
& {\text{factors}} \cr
& {\left( {x - 1} \right)^2}{\text{ and }}{x^2} + 1 \cr
& {\left( {x - 1} \right)^2}{\text{, repeated linear factor}} \cr
& {x^2} + 1,{\text{ irreductible quadratic factor}} \cr
& \cr
& {\text{the partial fraction decomposition is}} \cr
& \frac{{20x}}{{{{\left( {x - 1} \right)}^2}\left( {{x^2} + 1} \right)}} = \frac{A}{{x - 1}} + \frac{B}{{{{\left( {x - 1} \right)}^2}}} + \frac{{Cx + D}}{{{x^2} + 1}} \cr} $$