Solve x+5/x-3>0

$$\frac { x + 5 } { x - 3 } > 0$$

Solve for x

$$x\in \left(-\infty,-5\right)\cup \left(3,\infty\right)$$

Solution Steps

For the quotient to be positive, x+5 and x-3 have to be both negative or both positive. Consider the case when x+5 and x-3 are both negative.

$$x+5<0 x-3<0$$

The solution satisfying both inequalities is x<-5.

$$x<-5$$

Consider the case when x+5 and x-3 are both positive.

$$x-3>0 x+5>0$$

The solution satisfying both inequalities is x>3.

$$x>3$$

The final solution is the union of the obtained solutions.

$$x<-5\text{; }x>3$$