Solve 1+a/1-a<0

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

Solve for a

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

Solution Steps

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

$$a+1>0 1-a<0$$

The solution satisfying both inequalities is a>1.

$$a>1$$

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

$$1-a>0 a+1<0$$

The solution satisfying both inequalities is a<-1.

$$a<-1$$

The final solution is the union of the obtained solutions.

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