Solve x-1/x+1<1

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

Solve for x

$$x>-1$$

Solution Steps

Denominator x+1 cannot be zero since division by zero is not defined. There are two cases.

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

Consider the case when x+1 is positive. Move 1 to the right hand side.

$$x>-1$$

The initial inequality does not change the direction when multiplied by x+1 for x+1>0.

$$x-1<x+1$$

Move the terms containing x to the left hand side and all other terms to the right hand side.

$$x-x<1+1$$

Combine like terms.

$$0<2$$

Consider condition x>-1 specified above.

$$x>-1$$

Now consider the case when x+1 is negative. Move 1 to the right hand side.

$$x<-1$$

The initial inequality changes the direction when multiplied by x+1 for x+1<0.

$$x-1>x+1$$

Move the terms containing x to the left hand side and all other terms to the right hand side.

$$x-x>1+1$$

Combine like terms.

$$0>2$$

Consider condition x<-1 specified above.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x>-1$$