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What numbers for which the rational expression is undefined? \frac{8}{9x + 7}

Question:

What numbers for which the rational expression is undefined?

{eq}\displaystyle \frac{8}{9x + 7} {/eq}

Rational Expression:

A rational expression is a fraction where the numerator and the denominator are expressions of a variable. Since a fraction with a denominator 0 is not defined, a rational expression is undefined when its denominator is zero.

Answer and Explanation:

The given rational expression is:

$$\frac{8}{9x + 7} $$

A rational expression is undefined when its denominator is zero.

So we set the denominator to zero:

$$9x+7=0 \\ \text{Subtracting 7 from both sides}, \\ 9x =-7 \\ \text{Dividing both sides by 9}, \\ x= \dfrac{-7}{9} $$

Therefore, the given rational expression is NOT defined at {eq}\boxed{\mathbf{x= \dfrac{-7}{9}}} {/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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