The solution set of the inequality |x+2|−xx<2 is

We have |x+2|−xx<2⇒ |x+2|−3xx<0Let |x+2|−3x=0⇒ x+2=±3x⇒ x=1Sign scheme of the expression |x+2|−3xx is as shown in the following figure:  From the sign scheme, x∈(−∞,0)∪(1,∞)