# What is the undefined value of { \frac{(3b^2 + 13b + 4)}{(b + 4)} }

## Question:

What is the undefined value of {eq}\frac{(3b^2 + 13b + 4)}{(b + 4)} {/eq}

## Undefined Value:

- The undefined value of a rational expression is a value of the variable where the expression is NOT defined.
- For example, a fraction {eq}\dfrac{1}{x} {/eq} is not defined when its denominator is zero. i.e., when {eq}x=0 {/eq}.

## Answer and Explanation:

The given fraction is:

$$\frac{3b^2 + 13b + 4}{b + 4} $$

To find the undefined value, we set the denominator to zero and solve (as a fraction is NOT defined when its denominator is zero):

$$b+4=0\\[0.3cm] $$

Subtracting {eq}4{/eq} from both sides,

$$\color{blue}{\boxed{\mathbf{b=-4}}} $$

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Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 9
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