Solve x+2/1-x<0

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

Solve for x

$$x\in \left(-\infty,-2\right)\cup \left(1,\infty\right)$$

Solution Steps

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

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

The solution satisfying both inequalities is x>1.

$$x>1$$

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

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

The solution satisfying both inequalities is x<-2.

$$x<-2$$

The final solution is the union of the obtained solutions.

$$x>1\text{; }x<-2$$