Answer
$\frac{-x+2}{x^2+1}$
Work Step by Step
$-\frac{1}{x}+\frac{2}{x^2+1}+\frac{1}{x^3+x}=-\frac{x^2+1}{x(x^2+1)}+\frac{2x}{(x^2+1)x}+\frac{1}{x(x^2+1)}=\frac{-(x^2+1)+2x+1}{x(x^2+1)}=\frac{-x^2-1+2x+1}{x(x^2+1)}=\frac{-x^2+2x}{x(x^2+1)}=\frac{-x+2}{x^2+1}$
