Question

Determine the values that are excluded in the following expressions. $$ \frac{x-3}{x^{2}+12} $$

Name: Problem 15, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-05-03T02:59:03-08:00
Duration: 1 min 35 s
Channel: Aditya Modi
Description: Determine the values that are excluded in the following expressions. (x-3)/(x^2+12)

   Determine the values that are excluded in the following expressions.
$$
\frac{x-3}{x^{2}+12}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 15

Instant Answer

Solved by Expert Aditya Modi

05/03/2020

Step 1

So, we need to solve the equation: x^2 + 12 = 0 x^2 = -12 Since there is no real number whose square is a negative number, there are no real values of x that would make the denominator equal to 0. Show more…

Show all steps

Thanks for your feedback!

Determine the values that are excluded in the following expressions. $$ \frac{x-3}{x^{2}+12} $$

Play audio

Feedback

Aditya Modi and 50 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solving Denominator Equal to Zero

Determining the excluded values in a rational function typically involves setting the denominator equal to zero and solving the resulting equation. The solutions, if they exist within the domain of interest (such as the real numbers), indicate the values that must be excluded from the domain.

Division by Zero

Division by zero is not allowed in mathematics, as it leads to undefined or indeterminate expressions. Therefore, any solution of the equation formed by setting the denominator equal to zero must be excluded from the domain of the expression.

Domain of Rational Expressions

This concept involves identifying the set of all possible input values for which a rational expression is defined. In rational expressions, it is crucial to avoid values that cause the denominator to be zero, as division by zero is undefined.

Please give Ace some feedback