Solve 1-x/x+2>0

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

Solve for x

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

Solution Steps

For the quotient to be positive, 1-x and x+2 have to be both negative or both positive. Consider the case when 1-x and x+2 are both negative.

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

This is false for any x.

$$x\in \emptyset$$

Consider the case when 1-x and x+2 are both positive.

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

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

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

The final solution is the union of the obtained solutions.

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