Solve 2m/m-2>0

$$\frac { 2 m } { m - 2 } > 0$$

Solve for m

$$m\in \left(-\infty,0\right)\cup \left(2,\infty\right)$$

Solution Steps

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

$$2m<0 m-2<0$$

The solution satisfying both inequalities is m<0.

$$m<0$$

Consider the case when 2m and m-2 are both positive.

$$m-2>0 2m>0$$

The solution satisfying both inequalities is m>2.

$$m>2$$

The final solution is the union of the obtained solutions.

$$m<0\text{; }m>2$$