We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Definition of Rational Expression

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Which of the following fractions is NOT equivalent to $- \frac{x-5}{2x + 3}$ ?

Possible Answers:

$\frac{x-5}{\left -(2x+3 \right )}$

$\frac{x-5}{-2x-3}$

$\frac{\left -(x-5 \right )}{2x+3}$

$\frac{x+5}{2x + 3}$

$\frac{-x+5}{2x+3}$

Correct answer:

$\frac{x+5}{2x + 3}$

Explanation:

We know that $-\frac{a}{b}$ is equivalent to $\frac{-a}{b}$ or $\frac{a}{-b}$ .

By this property, there is no way to get $\frac{x+5}{2x+3}$ from $-\frac{x-5}{2x+3}$ .

Therefore the correct answer is $\frac{x+5}{2x+3}$ .

Report an Error

Example Question #1662 : Algebra Ii

Determine the domain of

$\frac{x+1}{x-1}$

Possible Answers:

$x\neq-1$

$x\neq1$

x=1

All real numbers

Correct answer:

$x\neq1$

Explanation:

Because the denominator cannot be zero, the domain is all other numbers except for 1, or

$x\neq1$

Report an Error

Example Question #2 : Definition Of Rational Expression

Simplify:

$\frac{x^2-1}{x^2+4x+2}\div\frac{x^2+2x+1}{x^2+3x+2}$

Possible Answers:

$\frac{x+2}{x+1}$

$\frac{1}{\frac{1}{x+1}}$

$\frac{x-1}{x+2}$

x-1

$\frac{x+2}{x-1}$

Correct answer:

$\frac{x-1}{x+2}$

Explanation:

This problem is a lot simpler if we factor all the expressions involved before proceeding:

$\frac{x^2-1}{x^2+4x+2}\div\frac{x^2+2x+1}{x^2+3x+2} \vspace{5mm}\\ = \frac{(x+1)(x-1)}{(x+2)(x+2)}\div\frac{(x+1)(x+1)}{(x+2)(x+1)}$

Next let's remember how we divide one fraction by another—by multiplying by the reciprocal:

$\frac{(x+1)(x-1)}{(x+2)(x+2)}\div\frac{(x+1)(x+1)}{(x+2)(x+1)} \vspace{5mm}\\ = \frac{(x+1)(x-1)}{(x+2)(x+2)}\times\frac{(x+2)(x+1)}{(x+1)(x+1)}$

In this form, we can see that a lot of terms are going to start canceling with each other. All that we're left with is just $\frac{x-1}{x+2}$ .

Report an Error

Example Question #3 : Definition Of Rational Expression

Which of the following is the best definition of a rational expression?

Possible Answers:

$\textup{The ratio of any two imaginary numbers.}$

$\textup{The ratio of any two real numbers.}$

$\textup{The ratio of two polynomials that must be different from each other.}$

$\textup{The ratio of two polynomials that cannot have a zero denominator.}$

$\textup{The ratio of two fractions that may have a zero denominator.}$

Correct answer:

$\textup{The ratio of two polynomials that cannot have a zero denominator.}$

Explanation:

The rational expression is a ratio of two polynomials.

$\frac{A(x)}{B(x)}$

The denominator cannot be zero.

An example of a rational expression is:

$\frac{x^2+x-5}{x+8}$

The answer is:

$\textup{The ratio of two polynomials that cannot have a zero denominator.}$

Report an Error

View Algebra 2 Tutors

Essence
Certified Tutor

University of Illinois at Urbana-Champaign, Masters in Business Administration, Business, General.

View Algebra 2 Tutors

Samantha
Certified Tutor

Southern New Hampshire University, Bachelor of Science, Psychology.

View Algebra 2 Tutors

Jose
Certified Tutor

Boston University, Bachelor of Science, Engineering and Industrial Management. Webster University, Masters in Business Admini...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Washington DC, MCAT Tutors in Boston, Computer Science Tutors in Houston, SSAT Tutors in Philadelphia, French Tutors in Dallas Fort Worth, ACT Tutors in Miami, SAT Tutors in San Diego, GRE Tutors in Philadelphia, Computer Science Tutors in New York City, ISEE Tutors in Boston

Popular Courses & Classes

GRE Courses & Classes in Denver, Spanish Courses & Classes in Miami, MCAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in San Diego, ACT Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC, SSAT Courses & Classes in Los Angeles, GRE Courses & Classes in Phoenix, GRE Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City

Popular Test Prep

SAT Test Prep in New York City, SSAT Test Prep in Boston, ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Washington DC, MCAT Test Prep in Seattle, SSAT Test Prep in Miami, SSAT Test Prep in Los Angeles, SSAT Test Prep in Phoenix, SSAT Test Prep in Atlanta, GMAT Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Definition of Rational Expression

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Example Question #1662 : Algebra Ii

Example Question #2 : Definition Of Rational Expression

Example Question #3 : Definition Of Rational Expression

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: