Solve m+1/m>0

$$\frac { m + 1 } { m } > 0$$

Solve for m

$$m\in \left(-\infty,-1\right)\cup \left(0,\infty\right)$$

Solution Steps

For the quotient to be positive, m+1 and m have to be both negative or both positive. Consider the case when m+1 and m are both negative.

$$m+1<0 m<0$$

The solution satisfying both inequalities is m<-1.

$$m<-1$$

Consider the case when m+1 and m are both positive.

$$m>0 m+1>0$$

The solution satisfying both inequalities is m>0.

$$m>0$$

The final solution is the union of the obtained solutions.

$$m<-1\text{; }m>0$$