We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Multiplying and Dividing Rational Expressions

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

← Previous 1 2 3 4 Next →

Example Question #21 : Multiplying And Dividing Rational Expressions

$\frac{\frac{4}{x}}{\frac{6}{x^2}}$

Possible Answers:

$\frac{2x^2}{3}$

$\frac{x}{3}$

$\frac{2x}{3}$

$\frac{2}{3}$

$\frac{1}{3}$

Correct answer:

$\frac{2x}{3}$

Explanation:

In this problem, we're dealing with dividing rational expressions. Therefore, we have to flip the second fraction and then multiply the two: $\frac{4}{x}\cdot \frac{x^2}{6}$ . Simplify and multiply straight across to get your answer: $\frac{2x}{3}$ .

Report an Error

Example Question #71 : Solving Rational Expressions

$\frac{2a}{b^2}\cdot \frac{5b^4}{10a}$

Possible Answers:

b^2

$\frac{1}{b^2}$

b^4

Correct answer:

b^2

Explanation:

When multiplying fractions, you will multiply straight across.

But first, see if you can reduce diagonally.

The a's cross out, and you can take out a b^2 from the other diagonal.

The coefficients also reduce.

$\frac{2a}{b^2}\cdot \frac{5b^4}{10a}=\frac{2}{1}\cdot \frac{b^2}{2}=b^2$

Therefore, your answer is b^2 .

Report an Error

Example Question #23 : Multiplying And Dividing Rational Expressions

Multiply: $\frac{3x}{x-3}\cdot \frac{x+3}{x-3}$

Possible Answers:

$\frac{ 3x^2+9}{x^2-9}$

$\frac{ 27x^3}{x^2-6x+9}$

$\frac{ 3x^2+9x}{x-3}$

$\frac{4x+3}{x-3}$

$\frac{ 3x^2+9x}{x^2-6x+9}$

Correct answer:

$\frac{ 3x^2+9x}{x^2-6x+9}$

Explanation:

Multiply the numerator with the numerator and denominator with the denominator.

Use the distributive property to expand the numerator.

3x(x+3) = 3x^2+9x

Use the FOIL method to simplify the denominator.

(x-3)(x-3)= x^2+(-3)(x)+(-3)(x)+(-3)(-3)

x^2-6x+9

Divide the numerator with the denominator. There are no common factors.

The answer is: $\frac{ 3x^2+9x}{x^2-6x+9}$

Report an Error

Example Question #24 : Multiplying And Dividing Rational Expressions

Simplify: $\frac{x^2-2x}{2x}\cdot \frac{x^2}{x^2-x-2}$

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Factor all the binomial and trinomial in the expression.

$\frac{x^2-2x}{2x}\cdot \frac{x^2}{x^2-x-2} = \frac{x(x-2)}{2x}\cdot \frac{x^2}{(x-2)(x+1)}$

Cancel all the common terms.

The expression becomes:

$\frac{x^2}{2(x+1)} = \frac{x^2}{2x+2}$

The answer is: $\frac{x^2}{2x+2}$

Report an Error

Example Question #25 : Multiplying And Dividing Rational Expressions

Divide: $\frac{x^2-1}{x}\div \frac{x^2}{x+1}$

Possible Answers:

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

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

x^2-x

x^2+x

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

Correct answer:

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

Explanation:

To divide this expression, take the reciprocal of the second term and change the division sign to a multiplication sign.

$\frac{x^2-1}{x}\div \frac{x^2}{x+1} = \frac{x^2-1}{x}\times \frac{x+1}{x^2} = \frac{(x^2-1)(x+1)}{x^3}$

Expand the numerator by FOIL method.

(x^2-1)(x+1) = (x^2)(x)+(x^2)(1)+(-1)(x)+(-1)(1)

x^3+x^2-x-1

Divide this by the denominator.

The answer is: $\frac{x^3+x^2-x-1}{x^3}$

Report an Error

Example Question #26 : Multiplying And Dividing Rational Expressions

Solve: $\frac{x+3}{x^2}\div\frac{x^4}{3}$

Possible Answers:

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

$\frac{3x+9}{x^6}$

$\frac{3x+3}{x^6}$

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

$\frac{3x+9}{x^8}$

Correct answer:

$\frac{3x+9}{x^6}$

Explanation:

In order to divide the rational expressions, we will need to convert the division sign to a multiplication sign and take the reciprocal of the second term.

$\frac{x+3}{x^2}\div\frac{x^4}{3} = \frac{x+3}{x^2} \times \frac{3} {x^4}$

Multiply the numerator with the numerator and denominator with the denominator.

3(x+3)=3x+9

x^2(x^4) = x^6

The answer is: $\frac{3x+9}{x^6}$

Report an Error

Example Question #27 : Multiplying And Dividing Rational Expressions

Divide: $\frac{3x+3}{6x-7}\div \frac{6}{x}$

Possible Answers:

$\frac{18x-18}{6x^2-7}$

$\frac{x^2+x}{12x-14}$

$\frac{x^2-x}{12x-14}$

$\frac{18x+18}{6x^2-7}$

$\frac{x^2-1}{12x-14}$

Correct answer:

$\frac{x^2+x}{12x-14}$

Explanation:

To divide the rational expression, we will need to take the reciprocal of the second term and change the division sign to a multiplication sign.

$\frac{3x+3}{6x-7}\div \frac{6}{x} = \frac{3x+3}{6x-7}\times \frac{x}{6}$

Multiply the numerator with the numerator and the denominator with the denominator.

x(3x+3) = 3x^2+3x

6(6x-7) =36x-42

Divide the numerator and denominator.

$\frac{ 3x^2+3x}{36x-42}$

Take out a three as a common factor.

$\frac{ 3x^2+3x}{36x-42}=\frac{3(x^2+x)}{3(12x-14)}=\frac{x^2+x}{12x-14}$

The answer is: $\frac{x^2+x}{12x-14}$

Report an Error

Example Question #28 : Multiplying And Dividing Rational Expressions

Divide: $\frac{x^3-1}{x+1} \div \frac{1}{x-1}$

Possible Answers:

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

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

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

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

$\frac{x^4+x^3+x+1}{x+1}$

Correct answer:

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

Explanation:

Be very careful not to apply the difference of cubes to simplify this expression!

Change the sign to multiplication and take the reciprocal of the second term.

$\frac{x^3-1}{x+1} \div \frac{1}{x-1}=\frac{x^3-1}{x+1} \cdot\frac{ x-1}{1}$

Multiply the top by FOIL method.

(x^3-1)(x-1) = (x^3)(x)+(x^3)(-1)+(-1)(x)+(-1)(-1)

x^4-x^3-x+1

Divide this by the denominator.

The answer is: $\frac{x^4-x^3-x+1}{x+1}$

Report an Error

Example Question #29 : Multiplying And Dividing Rational Expressions

Simplify: $\frac{x}{x-9}\div\frac{x-9}{x-18}$

Possible Answers:

$\frac{x^2-18}{x^2-18+81}$

$\frac{x+2}{x-9}$

$\frac{x}{x-18}$

$\frac{x+9}{x^2-18+81}$

$\frac{x-18}{x}$

Correct answer:

$\frac{x^2-18}{x^2-18+81}$

Explanation:

In order to simplify the rational expression, we will need to rewrite the expression as a multiplication sign and take the reciprocal of the second term.

$\frac{x}{x-9}\div\frac{x-9}{x-18}= \frac{x}{x-9} \times \frac{x-18}{x-9}$

Simplify the numerator.

x(x-18) = x^2-18x

Simplify the denominator by FOIL method.

(x-9)(x-9)= x^2-9x-9x+81 = x^2-18x+81

Divide the numerator with the denominator.

The answer is: $\frac{x^2-18}{x^2-18+81}$

Report an Error

Example Question #30 : Multiplying And Dividing Rational Expressions

Simplify: $\frac{x^2-x}{x^3-x} \cdot \frac{x+1}{x-1}$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Rewrite the left fraction using common factors.

$\frac{x^2-x}{x^3-x} \cdot \frac{x+1}{x-1} = \frac{x(x-1)}{x(x^2-1)} \cdot \frac{x+1}{x-1}$

Cancel out common terms.

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

Factorize the bottom term.

$\frac{x+1}{x^2-1} =\frac{x+1}{(x+1)(x-1)} = \frac{1}{x-1}$

The answer is: $\frac{1}{x-1}$

Report an Error

← Previous 1 2 3 4 Next →

View Algebra 2 Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

View Algebra 2 Tutors

Alena
Certified Tutor

Mogilevsky State Pedagogical Institute, Bachelor in Arts, Mathematics. Mogilevsky State Pedagogical Institute, Masters, Mathe...

View Algebra 2 Tutors

Jitendra
Certified Tutor

BHU, Bachelor, Mathematics.

All Algebra II Resources

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

Popular Subjects

Statistics Tutors in Atlanta, Computer Science Tutors in New York City, Algebra Tutors in Denver, French Tutors in Denver, ISEE Tutors in Phoenix, Physics Tutors in Atlanta, Statistics Tutors in Phoenix, Computer Science Tutors in San Diego, LSAT Tutors in Houston, Chemistry Tutors in Los Angeles

Popular Courses & Classes

MCAT Courses & Classes in Atlanta, LSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Phoenix, SAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Seattle, ACT Courses & Classes in Philadelphia, Spanish Courses & Classes in Seattle, ACT Courses & Classes in Phoenix, GMAT Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in Phoenix, LSAT Test Prep in Los Angeles, SSAT Test Prep in New York City, LSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in Miami, SAT Test Prep in San Diego, MCAT Test Prep in Boston, LSAT Test Prep in New York City, SSAT Test Prep in Boston, SSAT Test Prep in Philadelphia

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 : Multiplying and Dividing Rational Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Multiplying And Dividing Rational Expressions

Example Question #71 : Solving Rational Expressions

Example Question #23 : Multiplying And Dividing Rational Expressions

Example Question #24 : Multiplying And Dividing Rational Expressions

Example Question #25 : Multiplying And Dividing Rational Expressions

Example Question #26 : Multiplying And Dividing Rational Expressions

Example Question #27 : Multiplying And Dividing Rational Expressions

Example Question #28 : Multiplying And Dividing Rational Expressions

Example Question #29 : Multiplying And Dividing Rational Expressions

Example Question #30 : Multiplying And Dividing Rational Expressions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: