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}.

Answer and Explanation:

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}.


Learn more about this topic:

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Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4
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