Solve 1-x/1+x<0

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

Solve for x

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

Solution Steps

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

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

The solution satisfying both inequalities is x<-1.

$$x<-1$$

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

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

The solution satisfying both inequalities is x>1.

$$x>1$$

The final solution is the union of the obtained solutions.

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