Solve x-1/x-2<0

$$\frac { x - 1 } { x - 2 } < 0$$

Solve for x

$$x\in \left(1,2\right)$$

Solution Steps

For the quotient to be negative, x-1 and x-2 have to be of the opposite signs. Consider the case when x-1 is positive and x-2 is negative.

$$x-1>0 x-2<0$$

The solution satisfying both inequalities is x\in \left(1,2\right).

$$x\in \left(1,2\right)$$

Consider the case when x-2 is positive and x-1 is negative.

$$x-2>0 x-1<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(1,2\right)$$