Which of the following is the correct form of the partial fraction decomposition of $\displaystyle \frac{x-1}{x^3+x}?$

A. $\displaystyle \frac{Ax+B}{x}+\frac{C}{x^2+1}$
B. $\displaystyle \frac{A}{x}+\frac{Bx+C}{x^2+1}$
C. $\displaystyle \frac{A}{x}+\frac{B}{x^2+1}$
D. $\displaystyle \frac{Ax+B}{x}+\frac{Cx+D}{x^2+1}$