GRE Math : How to subtract rational expressions with different denominators

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #281 : Algebra

Choose the answer which best simplifies the following expression:

$\frac{2p^2 + 3p}{2a} - \frac{5p}{3}$

Possible Answers:

$\frac{6p^2 + 9p -10p}{6}$

$\frac{6p + 9p -10pa}{6a}$

$\frac{6p^2 + 9p -10pa}{6a}$

$\frac{6p^2 + 9p +10pa}{6a}$

$\frac{15p -10pa}{6a}$

Correct answer:

$\frac{6p^2 + 9p -10pa}{6a}$

Explanation:

To simplify this expression, first multiply both terms by the denominator of the other over itself:

$\frac{2p^2 + 3p}{2a}\left(\frac{3}{3}\right) - \frac{5p}{3}\left(\frac{2a}{2a}\right)$

$\frac{6p^2 + 9p}{6a} - \frac{10pa}{6a}$

Now that you have a common denominator, you may subtract:

$\frac{6p^2 +9p - 10pa}{6a}$

Report an Error

Example Question #11 : Rational Expressions

Choose the answer which best simplifies the following expression:

$\frac{2n + 4}{n} - \frac{n^2}{5}$

Possible Answers:

$\frac{-n^3+10n+20}{-5n}$

$\frac{n^3+10n+20}{5n}$

$\frac{-n^2+10n+20}{5n}$

$\frac{-n^3+10n+20}{5n}$

$\frac{-n^3-10n-20}{5n}$

Correct answer:

$\frac{-n^3+10n+20}{5n}$

Explanation:

To simplify this problem, multiply each term by the denominator of the other over itself:

$\frac{2n + 4}{n}\left(\frac{5}{5}\right) - \frac{n^2}{5}\left(\frac{n}{n}\right)$

$\frac{10n + 20}{5n} - \frac{n^3}{5n}$

Now that both terms share a denominator, you can subtract:

$\frac{-n^3+10n+20}{5n}$

Report an Error

Example Question #11 : Rational Expressions

Choose the answer which best simplifies the following expression:

$\frac{2x + a}{4} - \frac{3}{2a}$

Possible Answers:

$\frac{2ax + a^2 - 6}{4a^2}$

$\frac{4ax + 2a^2 - 12}{8a}$

$\frac{2a^2x + a^2 - 6}{4a}$

$\frac{2ax + a^2 - 6}{4a}$

$\frac{2ax + a^2 - 6x}{4a}$

Correct answer:

$\frac{2ax + a^2 - 6}{4a}$

Explanation:

To solve this problem, first multiply each term of the original expression by the denomenator of the other over itself:

$\frac{2x + a}{4}(\frac{2a}{2a}) - \frac{3}{2a}(\frac{4}{4})$

Then you will have two terms with a common denomenator:

$\frac{4ax + 2a^2}{8a} - \frac{12}{8a}$

Combine the terms and simplify for your final answer:

$\frac{4ax +2a^2 - 12}{8a}$

$\frac{2ax + a^2 - 6}{4a}$

Report an Error

Example Question #292 : Algebra

Choose the answer which best simplifies the expression below:

$\frac{2p^2 - 3p}{b} - \frac{b^2}{p}$

Possible Answers:

$\frac{2p^2 - 3p -b^3}{pb}$

$\frac{2p^3 - 3p^2 -b^3}{pb}$

$\frac{2p^3 - 3p^2 -b^3}{p}$

$\frac{2p^3 - 3p^2 -b^3}{b}$

$\frac{2p - 3p^2 -b^3}{pb}$

Correct answer:

$\frac{2p^3 - 3p^2 -b^3}{pb}$

Explanation:

To simplify this problem, multiply each term by the denomenator of the other over itself:

$\frac{2p^2 - 3p}{b}(\frac{p}{p}) - \frac{b^2}{p}(\frac{b}{b})$

Then you will yield terms with a like denomenator, which can be combined:

$\frac{2p^3 - 3p^2}{pb} - \frac{b^3}{pb}$

$\frac{2p^3 - 3p^2 - b^3}{pb}$

Report an Error

Example Question #293 : Algebra

Choose the answer which best simplifies the expression below:

$\frac{xy^2}{m} - \frac{m^2n}{y}$

Possible Answers:

$\frac{xy^3 - m^3n}{my}$

$\frac{xy^2 - m^2n}{my}$

$\frac{xy^3 - m^3n}{m}$

$\frac{x(y^3 - m^3n)}{my}$

$\frac{xy^3 - m^3n}{y}$

Correct answer:

$\frac{xy^3 - m^3n}{my}$

Explanation:

To simplify the expression, first multiply each term by the denomenator of the other over itself:

$\frac{xy^2}{m}(\frac{y}{y}) - \frac{m^2n}{y}(\frac{m}{m})$

Then you yield terms with common denomenators, which can be combined:

$\frac{xy^3}{my}-\frac{m^3n}{my}$

$\frac{xy^3 - m^3n}{my}$

Report an Error

Example Question #11 : Rational Expressions

Choose the answer which best simplifies the following expression:

$\frac{x^2 + x + 3}{4a}-\frac{2y^2}{7}$

Possible Answers:

$\frac{7x^2 +7x +21-8ya}{28a}$

$\frac{7x^2 +7x +21-8y^2a}{7a}$

$\frac{7x^2 +7x +21-8y^2}{28a}$

$\frac{x^2 +x +3-8y^2a}{28a}$

$\frac{7x^2 +7x +21-8y^2a}{28a}$

Correct answer:

$\frac{7x^2 +7x +21-8y^2a}{28a}$

Explanation:

To simplify, first multiply each of the terms by the denomenator of the other over itself:

$\frac{x^2 + x + 3}{4a}(\frac{7}{7})-\frac{2y^2}{7}(\frac{4a}{4a})$

Then you will get terms with a common denomenator, which can be combined:

$\frac{7x^2 + 7x + 21}{28a}-\frac{8y^2a}{28a}$

$\frac{7x^2 +7x +21-8y^2a}{28a}$

Report an Error

Example Question #1 : How To Subtract Rational Expressions With Different Denominators

Choose the answer which best simplifies the expression below:

$\frac{2n^2 - n}{3a^2}-\frac{-n^2}{b}$

Possible Answers:

$\frac{2n^2b-nb-3a^2n^2}{3a^2b}$

$\frac{2n^2b-nb+3a^2n^2}{3ab}$

$\frac{2n^2b+nb+3a^2n^2}{3a^2b}$

$\frac{-2n^2b-nb-3a^2n^2}{3a^2b}$

$\frac{2n^2b-nb+3a^2n^2}{3a^2b}$

Correct answer:

$\frac{2n^2b-nb+3a^2n^2}{3a^2b}$

Explanation:

To simplify, first multiply each of the terms by the denomenator of the other over itself:

$\frac{2n^2 - n}{3a^2}(\frac{b}{b})-\frac{-n^2}{b}(\frac{3a^2}{3a^2})$

You will yield terms with a common denomenator, which can be combined:

$\frac{2n^2b - nb}{3a^2b}-\frac{-3a^2n^2}{3a^2b}$

$\frac{2n^2b-nb+3a^2n^2}{3a^2b}$

Report an Error

Example Question #11 : Expressions

Choose the answer which best simplifies the expression below:

$\frac{2a}{14-y} - \frac{3}{8 +a}$

Possible Answers:

$\frac{2a^2 +16a +3y +42}{112 - 8y+14a -ay}$

$\frac{2a^2 +16a -3y -42}{112 - 8y+14a -ay}$

$\frac{2a^2 +16a +3y -42}{112 - 8y+14a -ay}$

$\frac{2a^2 +16a +3y -42}{-112 - 8y+14a -ay}$

$\frac{2a^2 +16a +3y -42}{112 - 8y-14a -ay}$

Correct answer:

$\frac{2a^2 +16a +3y -42}{112 - 8y+14a -ay}$

Explanation:

To simplify, multiply each of the terms by the denomenator of the other, over itself:

$\frac{2a}{14-y}(\frac{8 +a}{8+a}) - \frac{3}{8 +a}(\frac{14-y}{14-y})$

You will yield terms with a common denomenator, which can be combined:

$\frac{16a +2a^2}{112-8y+14a-ay}-\frac{42-3y}{112-8y+14a-ay}$

$\frac{2a^2 +16a +3y -42}{112 - 8y+14a -ay}$

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in Washington DC, LSAT Tutors in San Francisco-Bay Area, English Tutors in Denver, MCAT Tutors in Miami, Statistics Tutors in Philadelphia, Biology Tutors in Chicago, Physics Tutors in Denver, ISEE Tutors in Boston, Biology Tutors in Houston, English Tutors in Seattle

Popular Courses & Classes

SSAT Courses & Classes in Boston, SAT Courses & Classes in Houston, Spanish Courses & Classes in New York City, SAT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, Spanish Courses & Classes in Chicago, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Miami, ACT Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in Boston, SSAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Phoenix, SSAT Test Prep in Seattle, LSAT Test Prep in San Diego, GRE Test Prep in Chicago, SSAT Test Prep in Atlanta, MCAT Test Prep in Houston, ISEE Test Prep in Dallas Fort Worth, SSAT Test Prep in Washington DC

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)

Email address:
Your name:
Feedback:

GRE Math : How to subtract rational expressions with different denominators

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #281 : Algebra

Example Question #11 : Rational Expressions

Example Question #11 : Rational Expressions

Example Question #292 : Algebra

Example Question #293 : Algebra

Example Question #11 : Rational Expressions

Example Question #1 : How To Subtract Rational Expressions With Different Denominators

Example Question #11 : Expressions

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details