Solve x/x+3>09

$$\frac{ x }{ x+3 } > 09$$

Solve for x

$$x\in \left(-\infty,-3\right)\cup \left(0,\infty\right)$$

Solution Steps

Multiply 0 and 9 to get 0.

$$\frac{x}{x+3}>0$$

For the quotient to be positive, x and x+3 have to be both negative or both positive. Consider the case when x and x+3 are both negative.

$$x<0 x+3<0$$

The solution satisfying both inequalities is x<-3.

$$x<-3$$

Consider the case when x and x+3 are both positive.

$$x+3>0 x>0$$

The solution satisfying both inequalities is x>0.

$$x>0$$

The final solution is the union of the obtained solutions.

$$x<-3\text{; }x>0$$