Keep the sign of x when solving a rational inequality

For x≠0, $2/x-x-1=-(x+2)(x-1)/x$. Thus require $(x+2)(x-1)/x<0$. The critical values are −2,0,1; the interval signs are −,+,−,+. The solution set is $\{x\in\mathbb R:x<-2\text{ or }0<x<1\}$, retaining the printed answer. All three endpoints are excluded. This working explains the answer supplied in the self-practice box.