Solve -x-4/x-2>0

$$\frac { - x - 4 } { x - 2 } > 0$$

Solve for x

$$x\in \left(-4,2\right)$$

Solution Steps

For the quotient to be positive, -x-4 and x-2 have to be both negative or both positive. Consider the case when -x-4 and x-2 are both negative.

$$-x-4<0 x-2<0$$

The solution satisfying both inequalities is x\in \left(-4,2\right).

$$x\in \left(-4,2\right)$$

Consider the case when -x-4 and x-2 are both positive.

$$x-2>0 -x-4>0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(-4,2\right)$$