## College Algebra 7th Edition

The solution is all real numbers except $x=0$ and $x=-1/2$.
$\displaystyle \frac{1}{x}-\frac{2}{2x+1}=\frac{1}{2x^{2}+x}$ 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 $x=-1/2$.