Solve 1/x-1>0

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

Solve for x

$$x\in \left(0,1\right)$$

Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x}{x}.

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

Since \frac{1}{x} and \frac{x}{x} have the same denominator, subtract them by subtracting their numerators.

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

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

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

This is false for any x.

$$x\in \emptyset$$

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

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

The solution satisfying both inequalities is x\in \left(0,1\right).

$$x\in \left(0,1\right)$$

The final solution is the union of the obtained solutions.

$$x\in \left(0,1\right)$$