Solve x/x+2<0

$$\frac { x } { x + 2 } < 0$$

Solve for x

$$x\in \left(-2,0\right)$$

Solution Steps

For the quotient to be negative, x and x+2 have to be of the opposite signs. Consider the case when x is positive and x+2 is negative.

$$x>0 x+2<0$$

This is false for any x.

$$x\in \emptyset$$

Consider the case when x+2 is positive and x is negative.

$$x+2>0 x<0$$

The solution satisfying both inequalities is x\in \left(-2,0\right).

$$x\in \left(-2,0\right)$$

The final solution is the union of the obtained solutions.

$$x\in \left(-2,0\right)$$