We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Least Common Denominator

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 #11 : Least Common Denominator

Find the least common denominator between $\frac{x-9}{2x+1}$ and $\frac{x^2}{3x+9}$

Possible Answers:

6x^2+9

5x+10

6x^2+18

6x^2+21x+9

Correct answer:

6x^2+21x+9

Explanation:

To find the least common denominator, multply the two denominators together.

(2x+1)(3x+9)=6x^2+21x+9

Report an Error

Example Question #12 : Least Common Denominator

Find the least common denominator between $\frac{x^2-2}{x+4}$ and $\frac{3x^2-2}{x-9}$

Possible Answers:

x^2-13x-36

x^2-5x-36

x^2+5x-36

x^2-36

Correct answer:

x^2-5x-36

Explanation:

To find the least common denominator, multply the two denominators together.

(x-9)(x+4)=x^2-5x-36

Report an Error

Example Question #13 : Least Common Denominator

Find the least common denominator for $\frac{x-2}{x^2-4}$ and $\frac{x-3}{x^2-9}$ .

Possible Answers:

x-4

x^2+5x+6

x^2+6

x^2-5x-6

Correct answer:

x^2+5x+6

Explanation:

Start by simplifying both fractions.

$\frac{x-2}{x^2-4}=\frac{x-2}{(x-2)(x+2)}=\frac{1}{x+2}$

$\frac{x-3}{x^2-9}=\frac{x-3}{(x-3)(x+3)}=\frac{1}{x+3}$

Now, to find the least common denominator for the two simplified fractions, multiply the denominators together.

(x+2)(x+3)=x^2+5x+6

Report an Error

Example Question #31 : Understanding Rational Expressions

What is the least common denominator for the following fractions?

$\small \frac{1}{4},\frac{2}{3},\frac{1}{6},\frac{3}{8},\frac{5}{12}$

Possible Answers:

Correct answer:

Explanation:

Remember that the least common denominator is the smallest number such that all fractions' denominators divide it evenly.

Always start with the largest number. In this case, it is 12. 3, 4, 6, and 12 all divide evenly into 12, but 8 does not. Think of the next multiple of the largest number. In this case, 24. Here we see that 3, 4, 6, 8, and 12 all divide 24 evenly. Thus, our least common denominator is 24.

Report an Error

Example Question #32 : Rational Expressions

Simplify:

$\frac{4}{x}+\frac{3}{x+5}+\frac{1}{x^2+5x}$

Possible Answers:

$\frac{7x+21}{x^2+5x}$

$\frac{28}{x+5}$

$\frac{7x+6}{x^2+5x}$

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

Correct answer:

$\frac{7x+21}{x^2+5x}$

Explanation:

To simplify the expression, we must find the common denominator, which in this case is

x(x+5)

Note that when we distribute the x, we get the denominator of the third term, x^2+5x .

Now, we multiply each term by the LCD divided by itself:

$\frac{x(x+5)}{x(x+5)}\cdot \frac{4}{x}+\frac{x(x+5)}{x(x+5)}\cdot \frac{3}{x+5}+\frac{x(x+5)}{x(x+5)}\cdot \frac{1}{x^2+5x}$

Which, after some canceling, becomes

$\frac{4(x+5)}{x(x+5)}+\frac{3(x)}{x(x+5)}+\frac{1}{x^2+5x}$

Now that all of the terms have the same denominator, we can add their numerators together:

$\frac{4(x+5)+3x+1}{x^2+5x}=\frac{4x+20+3x+1}{x^2+5x}=\frac{7x+21}{x^2+5x}$

Report an Error

Example Question #16 : Least Common Denominator

What is the least common denominator of the following fractions?

$\frac{2}{3x}+\frac{3}{2+x}-\frac{1}{6}$

Possible Answers:

18x^2+36x

10x^2+2

3x^2+6x

3x^2+3x+8

4x+8

Correct answer:

18x^2+36x

Explanation:

In order to determine the least common denominator, multiply all the uncommon denominators together.

3x(2+x)(6)

Use the distributive property to simplify these terms.

3x(2+x)(6) = (6x+3x^2)(6) = 36x+18x^2

The least common denominator is: 18x^2+36x

Report an Error

Example Question #17 : Least Common Denominator

What is the least common denominator needed to continue with the following problem?

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

Possible Answers:

$\frac{x+12}{x^2-x-6}$

x^2+5x-6

$-\frac{x+12}{x^2-x-6}$

x^2-x-6

Correct answer:

x^2-x-6

Explanation:

In order to continue to simplify this problem, we will need to multiply both denominators together in order to simplify the numerators.

Multiply both of the denominators by using the FOIL method.

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

Simplify this expression.

The least common denominator required is: x^2-x-6

Be careful not to continue and solve the problem!

The answer is: x^2-x-6

Report an Error

Example Question #18 : Least Common Denominator

Determine the least common denominator for: $\frac{1}{3x}-\frac{2}{3-x}+\frac{1}{3+x}$

Possible Answers:

x^3+3x-9

x^3+27x-3

-3x^3+27x+9

x^2+3

-3x^3+27x

Correct answer:

-3x^3+27x

Explanation:

Determine the least common denominator by multiplying the denominators together.

3x(3-x)(3+x)

Multiply the first two terms together.

9x-3x^2

Multiply this quantity with the third term.

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

Use the FOIL method to expand this expression.

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

Simplify and combine like terms.

27x+9x^2-9x^2-3x^3

The answer is: -3x^3+27x

Report an Error

Example Question #19 : Least Common Denominator

Determine the least common denominator: $\frac{1}{9-x}+\frac{2}{9-2x}$

Possible Answers:

-4x+27

4x-27

2x^2-27x-81

2x^2-27x+81

2x^2-81

Correct answer:

2x^2-27x+81

Explanation:

In order to determine the least common denominator, we will need to use the FOIL method to expand the denominators.

(9-x)(9-2x)

Multiply the terms.

(9)(9)+(9)(-2x)+(-x)(9)+(-x)(-2x)

81-18x-9x+2x^2

Combine like-terms.

The answer is: 2x^2-27x+81

Report an Error

Example Question #20 : Least Common Denominator

Determine the least common denominator: $\frac{1}{x^2y}+\frac{1}{x^2+y}$

Possible Answers:

x^2y

2xy+x^2y

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

x^4y+x^2y^2

x^2+y

Correct answer:

x^4y+x^2y^2

Explanation:

In order to determine the least common denominator, we will need to multiply both denominators together. Be careful not to mix up the denominators as similar entities.

x^2y(x^2+y) = x^4y+x^2y^2

Do not solve the problem.

The answer is: x^4y+x^2y^2

Report an Error

View Algebra 2 Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

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

Popular Subjects

ISEE Tutors in Houston, GMAT Tutors in Los Angeles, Physics Tutors in Phoenix, Algebra Tutors in New York City, ACT Tutors in San Diego, Spanish Tutors in Houston, MCAT Tutors in Denver, GMAT Tutors in Washington DC, SAT Tutors in Dallas Fort Worth, Biology Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Miami, GMAT Courses & Classes in Houston, ACT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Denver, SAT Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Washington DC, Spanish Courses & Classes in Philadelphia

Popular Test Prep

SSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Houston, GMAT Test Prep in New York City, MCAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Washington DC, ISEE Test Prep in Washington DC, SAT Test Prep in Washington DC, SSAT Test Prep in Los Angeles, GMAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Houston

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 : Least Common Denominator

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Least Common Denominator

Example Question #12 : Least Common Denominator

Example Question #13 : Least Common Denominator

Example Question #31 : Understanding Rational Expressions

Example Question #32 : Rational Expressions

Example Question #16 : Least Common Denominator

Example Question #17 : Least Common Denominator

Example Question #18 : Least Common Denominator

Example Question #19 : Least Common Denominator

Example Question #20 : Least Common Denominator

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: