Solve x+2/x-2>0

$$\frac { x + 2 } { x - 2 } > 0$$

Solve for x

$$x\in \left(-\infty,-2\right)\cup \left(2,\infty\right)$$

Solution Steps

For the quotient to be positive, x+2 and x-2 have to be both negative or both positive. Consider the case when x+2 and x-2 are both negative.

$$x+2<0 x-2<0$$

The solution satisfying both inequalities is x<-2.

$$x<-2$$

Consider the case when x+2 and x-2 are both positive.

$$x-2>0 x+2>0$$

The solution satisfying both inequalities is x>2.

$$x>2$$

The final solution is the union of the obtained solutions.

$$x<-2\text{; }x>2$$