Question

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

Answer 1

Solution: `-3 < x <8` , in interval notation: `(-3,8)`

Explanation:

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

Sign Change:

For `x < -3` , sign of `(x+3)/(x-8)` is `(-)/(-) = + i.e >0`

For `-3 < x <8` , sign of `(x+3)/(x-8)` is `(+)/(-) = - i.e <0`

For `x > 8` , sign of `(x+3)/(x-8)` is `(+)/(+) = + i.e >0`

So, Solution: `-3 < x <8` , in interval notation: `(-3,8)`

The graph also confirms above findings.

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