Disequazione fratta $\dfrac{x-2}{x+1}\ge 0$

Text

Solve the fractional inequality $\frac{x-2}{x+1}\ge 0.$

Solution

Key points: $x=2$ (numerator, included) and $x=-1$ (denominator, excluded). The ratio is $\ge 0$ where numerator and denominator have the same sign:

• $x<-1$: $(-)/(-)>0$;
• $-1<x<2$: $(-)/(+)<0$;
• $x\ge 2$: $(+)/(+)\ge 0$. $\boxed{x<-1\ \vee\ x\ge 2.}$