Solve x-7/x+8>0

$$\frac { x - 7 } { x + 8 } > 0$$

Solve for x

$$x\in \left(-\infty,-8\right)\cup \left(7,\infty\right)$$

Solution Steps

For the quotient to be positive, x-7 and x+8 have to be both negative or both positive. Consider the case when x-7 and x+8 are both negative.

$$x-7<0 x+8<0$$

The solution satisfying both inequalities is x<-8.

$$x<-8$$

Consider the case when x-7 and x+8 are both positive.

$$x+8>0 x-7>0$$

The solution satisfying both inequalities is x>7.

$$x>7$$

The final solution is the union of the obtained solutions.

$$x<-8\text{; }x>7$$