Solve x/x>0

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

Evaluate (complex solution)

$$x\neq 0$$

Solution Steps

Divide x by x to get 1.

$$1>0$$

Compare 1 and 0.

$$\text{true}$$

Solve for x

$$x\neq 0$$

Solution Steps

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

$$x<0 x<0$$

The solution satisfying both inequalities is x<0.

$$x<0$$

Consider the case when x and x are both positive.

$$x>0 x>0$$

The solution satisfying both inequalities is x>0.

$$x>0$$

The final solution is the union of the obtained solutions.

$$x\neq 0$$