Solve x/x-1>0

$$\frac { x } { x - 1 } > 0$$

Solve for x

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

Solution Steps

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

$$x<0 x-1<0$$

The solution satisfying both inequalities is x<0.

$$x<0$$

Consider the case when x and x-1 are both positive.

$$x-1>0 x>0$$

The solution satisfying both inequalities is x>1.

$$x>1$$

The final solution is the union of the obtained solutions.

$$x<0\text{; }x>1$$