Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

Previous problemNext problem

1:30 minutes

Problem 17

Textbook Question

Find the domain of each rational expression. x^2 - 1 / x + 1

Verified step by step guidance

Identify the rational expression: $ \frac{x^2 - 1}{x + 1} $.

Recall that the domain of a rational expression is all real numbers except where the denominator is zero.

Set the denominator equal to zero to find the values that are not in the domain: $ x + 1 = 0 $.

Solve the equation $ x + 1 = 0 $ to find the value of $ x $ that makes the denominator zero.

Exclude the value found in the previous step from the domain of the rational expression.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding rational expressions is crucial because they can have restrictions on their values, particularly when the denominator is zero, which leads to undefined expressions.

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational expressions, the domain excludes any values that make the denominator zero, as these would result in undefined expressions.

Finding Restrictions

To find the domain of a rational expression, one must identify the values that cause the denominator to equal zero. This involves solving the equation formed by the denominator and excluding these values from the domain, ensuring that the expression remains valid.