If S is the set of all real x such that $\frac{2x-1}{2x^3+3x^2+x}$  is positive, then S contains

We have  $f\left(x\right)=\frac{2x-1}{2x^2+3x^2+x}=\frac{2x-1}{x(2x+1)(x+1)}$
Critical points are $x=\frac{1}{2},0,-\frac{1}{2},-1$ On the number line by scheme method, we have
 
For $f\left(x\right)>0$ , when  $x\in (-\infty ,-1)\cup (\frac{-1}{2},0)\cup (\frac{1}{2},\infty )$
Clearly S contains   $(-\infty ,-\frac{3}{2})$and  $(\frac{1}{2},3)$
Therefore, (a) and (d) are the correct answers.