Answer
$\frac{5x^3-3x^2+7x-3}{(x^2+1)^2}$
Work Step by Step
$\frac{5x-3}{x^2+1}+\frac{2x}{(x^2+1)^2}=\frac{(5x-3)(x^2+1)}{(x^2+1)^2}+\frac{2x}{(x^2+1)^2}=\frac{(5x-3)(x^2+1)+2x}{(x^2+1)^2}=\frac{5x^3-3x^2+5x-3+2x}{(x^2+1)^2}=\frac{5x^3-3x^2+7x-3}{(x^2+1)^2}$