# Find all the numbers for which the rational expression is undefined { \frac{s^3-6x}{ s^2-9} }.

## Question:

Find all the numbers for which the rational expression is undefined {eq}\frac{s^3-6x}{ s^2-9} {/eq}.

## Excluded Value:

An excluded value of an expression is the value of a variable where the expression is not defined. For example, a fraction is not defined when its denominator is zero. So the excluded value of the fraction {eq}\dfrac{1}{x} {/eq} is {eq}x=0 {/eq}.

The given rational expression is,

$$\dfrac{s^3-6x}{ s^2-9}$$

To see where this is undefined, we set its denominator to zero and solve:

$$s^2-9=0 \\ \text{Adding 9 on both sides}, \\ s^2=9 \\ \text{Taking square root on both sides}, \\ s= \pm 3$$

Therefore, the given rational expression is undefined at {eq}\boxed{\mathbf{s=3 \text{ and } s=-3}} {/eq}.