# How do you solve (x+3)/(x-8)<0?

Jul 22, 2017

Solution: $- 3 < x < 8$ , in interval notation: $\left(- 3 , 8\right)$

#### Explanation:

 (x+3)/(x-8) < 0 ; x !=8  critical points are $x = 8 , x = - 3$

Sign Change:

For $x < - 3$ , sign of $\frac{x + 3}{x - 8}$ is $\frac{-}{-} = + i . e > 0$

For $- 3 < x < 8$ , sign of $\frac{x + 3}{x - 8}$ is $\frac{+}{-} = - i . e < 0$

For $x > 8$ , sign of $\frac{x + 3}{x - 8}$ is $\frac{+}{+} = + i . e > 0$

So, Solution: $- 3 < x < 8$ , in interval notation: $\left(- 3 , 8\right)$

The graph also confirms above findings.

graph{(x+3)/(x-8) [-11.25, 11.25, -5.625, 5.625]} [Ans]