Answer
The solution is all real numbers except $x=0$ and $x=-1/2$.
Work Step by Step
$\displaystyle \frac{1}{x}-\frac{2}{2x+1}=\frac{1}{2x^{2}+x}$
We multiply both sides by $(2x+1)(x)$:
$(2x+1)-2(x)=1$
And distribute:
$1=1$
When we get an identity (1=1, 2=2, x=x, etc), this implies that no matter what we choose for $x$, we will get a solution. Thus the solution should be all real numbers. However, if we use $x=0$ or $x=-1/2$, we would get division by 0 in the original equation. So these values are not allowed.
Thus the solution is all real numbers except $x=0$ and $x=-1/2$.
