We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Adding and Subtracting 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

Example Question #1742 : Algebra Ii

Subtract: $\frac{3}{8x}-\frac{6}{16-x}$

Possible Answers:

$\frac{51x-48}{8x^2+128}$

$\frac{12x-6}{8x+9}$

$\frac{51x+48}{8x^2+128}$

$\frac{51x+45}{8x^2+128}$

$\frac{51x-45}{8x^2+128}$

Correct answer:

$\frac{51x-48}{8x^2+128}$

Explanation:

In order to simplify this rational expression, we will need to determine the least common denominator.

8x(16-x) = 128x-8x^2

Convert the fractions.

$\frac{3(16-x)}{8x(16-x)}-\frac{6(8x)}{(16-x)(8x)}$

Simplify the fractions.

$\frac{48-3x}{ 128x-8x^2}-\frac{48x}{ 128x-8x^2}$

Simplify by combining like terms. Combine as one fraction.

$\frac{48-51x}{ 128x-8x^2}$

To rewrite this in the order of powers, we can factor a negative one on the top and bottom.

$\frac{-(-48+51x)}{- (128x+8x^2)} = \frac{51x-48}{8x^2+128}$

The answer is: $\frac{51x-48}{8x^2+128}$

Report an Error

Example Question #81 : Rational Expressions

Subtract: $\frac{1}{x}-\frac{x-3}{x^2+4x-21}$

Possible Answers:

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

$\frac{x-21}{x^3+4x^2-21x}$

$-\frac{x-7}{x^3+4x^2-21x}$

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

$\frac{x^2-4}{x^3+4x^2-21x}$

Correct answer:

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

Explanation:

Notice that the second fraction can be simplified. Factorize the denominator.

x^2+4x-21 = (x-3)(x+7)

Rewrite the expression.

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

Reduce the fraction.

$\frac{1}{x}-\frac{1}{x+7}$

Multiply both denominators together to determine the least common denominator.

x(x+7) =x^2+7x

Convert the fractions and solve.

$\frac{x+7}{x(x+7)}-\frac{x}{x(x+7)} = \frac{x+7}{x^2+7x}-\frac{x}{x^2+7x} =\frac{7}{x^2+7x}$

The answer is: $\frac{7}{x^2+7x}$

Report an Error

Example Question #82 : Rational Expressions

Add the expression: $\frac{3x}{x+1} + \frac{7}{9x}$

Possible Answers:

$\frac{27x^2+7x+7}{9x^2+9x}$

$\frac{3x^2+7}{9x^2+9x}$

$\frac{2x+22}{3x+3}$

$\frac{3x^2+3x+7}{3x^2+9x}$

$\frac{x+22}{3x+3}$

Correct answer:

$\frac{27x^2+7x+7}{9x^2+9x}$

Explanation:

Determine the least common denominator.

9x(x+1) = 9x^2+9x

Convert the fractions.

$\frac{3x(9x)}{(x+1)(9x)} + \frac{7(x+1)}{(9x)(x+1)}$

The expression becomes:

$\frac{3x(9x)+7(x+1)}{9x^2+9x} = \frac{27x^2+7x+7}{9x^2+9x}$

The answer is: $\frac{27x^2+7x+7}{9x^2+9x}$

Report an Error

Example Question #83 : Rational Expressions

Add: $\frac{9}{x}-\frac{x}{x-1}$

Possible Answers:

$-\frac{10}{x-1}$

$-\frac{x^2+9x+9}{x^2-1}$

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

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

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

Correct answer:

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

Explanation:

Determine the least common denominator.

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

Convert the fractions.

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

Simplify the numerator.

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

Combine as one fraction.

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

Pull out a common factor of negative one. This will allow us to pull the negative in front of the fraction.

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

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

Report an Error

Example Question #84 : Rational Expressions

Add: $\frac{1}{3x+9}+\frac{2}{x}$

Possible Answers:

$\frac{5x+9}{3x^2+9x}$

$\frac{5x+18}{3x^2+9x}$

$\textup{The answer is not given.}$

$\frac{5}{3x+9}$

$\frac{7x+18}{3x^2+9x}$

Correct answer:

$\frac{7x+18}{3x^2+9x}$

Explanation:

In order to add both terms, we will need to find the least common denominator.

Multiply the denominators together.

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

Convert the two fractions.

$\frac{1}{3x+9}+\frac{2}{x}=\frac{x}{3x^2+9x}+\frac{2(3x+9)}{3x^2+9x} =\frac{7x+18}{3x^2+9x}$

The answer is: $\frac{7x+18}{3x^2+9x}$

Report an Error

Example Question #85 : Rational Expressions

Subtract: $\frac{1}{3x}-\frac{3}{10x}$

Possible Answers:

$-\frac{1}{30x^2}$

$\frac{1}{30x}$

$-\frac{2}{7x}$

$\frac{1}{30}x$

$\frac{1}{30x^2}$

Correct answer:

$\frac{1}{30x}$

Explanation:

In order to subtract the numerators, we will need to determine the least common denominator. Upon visualization, the denominators share an x term. This means that we will not have to change the x term.

Multiply the first denominator by ten, and the second denominator by three.

$\frac{1}{3x}-\frac{3}{10x}=\frac{1(10)}{3x(10)}-\frac{3(3)}{10x(3)}$

Simplify the numerator.

$\frac{1(10)}{3x(10)}-\frac{3(3)}{10x(3)} = \frac{10}{30x}- \frac{9}{30x}$

The answer is: $\frac{1}{30x}$

Report an Error

Example Question #604 : Intermediate Single Variable Algebra

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

Possible Answers:

$-\frac{11x-10}{2x^2-2x}$

$-\frac{x+10}{2x^2-8x}$

$\frac{x+10}{2x^2-2x}$

$-\frac{4x+10}{2x^2-2x}$

$-\frac{11x-10}{2x^2-4x}$

Correct answer:

$-\frac{11x-10}{2x^2-4x}$

Explanation:

Multiply the denominators to get the least common denominator. We can then convert both fractions so that the denominators are alike.

$\frac{3}{2-x}-\frac{5}{2x}=\frac{3(2x)}{(2-x)(2x)}-\frac{5(2-x)}{2x(2-x)}$

Simplify both the top and the bottom.

$\frac{6x}{-2x^2+4x} - \frac{10-5x}{-2x^2+4x}$

Combine the numerators as one fraction. Be careful with the second fraction since the entire numerator is a quantity, which means we will need to brace 10-5x with parentheses.

$\frac{6x-(10-5x)}{-2x^2+4x} =\frac{6x-10+5x}{-2x^2+4x} = \frac{11x-10}{-2x^2+4x}$

Pull out a common factor of negative one in the denominator. This allows us to rewrite the fraction with the negative sign in front of the fraction.

$\frac{11x-10}{-2x^2+4x}= \frac{11x-10}{-(2x^2-4x)}= -\frac{11x-10}{2x^2-4x}$

The answer is: $-\frac{11x-10}{2x^2-4x}$

Report an Error

Example Question #611 : Intermediate Single Variable Algebra

Solve: $\frac{7}{5x}+\frac{9}{10x}$

Possible Answers:

$\frac{23}{10}x$

$\frac{25}{10}x$

$\frac{63}{50x}$

$\frac{25}{10x}$

$\frac{23}{10x}$

Correct answer:

$\frac{23}{10x}$

Explanation:

In order to solve this expression, we will need to determine the least common denominator. Notice that the denominators both share an x term. We do not need to change that.

Multiply the denominator of the first fraction by two to get the least common denominator, which is 10x .

$\frac{7(2)}{5x(2)}+\frac{9}{10x} = \frac{14}{10x}+\frac{9}{10x}$

Add the numerators.

The answer is: $\frac{23}{10x}$

Report an Error

Example Question #88 : Rational Expressions

Solve: $\frac{9x}{x+1}-\frac{9}{x}$

Possible Answers:

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

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

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

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

$\frac{9x}{x+1}$

Correct answer:

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

Explanation:

Determine the least common denominator by multiplying the denominators together.

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

Convert the fractions given.

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

Simplify the numerators and denominators.

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

Combine the terms as one fraction. Make sure to brace the 9x+9 term since this is a quantity.

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

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

Report an Error

Example Question #41 : Solving Rational Expressions

Add: $\frac{4x}{x-1}-\frac{10}{x}$

Possible Answers:

$\frac{4x^2-10x-10}{x^2-x}$

$\frac{4x^2-10}{x^2-x-10}$

$\frac{4x-10}{x-1}$

$\frac{4x+10}{x-1}$

$\frac{4x^2-10x+10}{x^2-x}$

Correct answer:

$\frac{4x^2-10x+10}{x^2-x}$

Explanation:

Identify the least common denominator by multiplying the denominators together.

Convert the fractions.

$\frac{4x}{x-1}-\frac{10}{x} = \frac{4x(x)}{x(x-1)}-\frac{10(x-1)}{x(x-1)}$

Simplify the numerator and denominator.

$\frac{4x^2}{x^2-x}-\frac{10x-10}{x^2-x}$

Combine both fractions as one. Make sure to enclose the second number in parentheses since the negative sign is distributive.

$\frac{4x^2}{x^2-x}-\frac{10x-10}{x^2-x}=\frac{4x^2-(10x-10)}{x^2-x} =\frac{4x^2-10x+10}{x^2-x}$

The answer is: $\frac{4x^2-10x+10}{x^2-x}$

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

SAT Tutors in Philadelphia, GMAT Tutors in Los Angeles, Physics Tutors in Atlanta, ISEE Tutors in San Francisco-Bay Area, Physics Tutors in Chicago, Calculus Tutors in Denver, LSAT Tutors in Seattle, ISEE Tutors in Phoenix, French Tutors in Atlanta, SSAT Tutors in Philadelphia

Popular Courses & Classes

MCAT Courses & Classes in San Diego, LSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Los Angeles, ACT Courses & Classes in Chicago, GRE Courses & Classes in Boston, Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in Miami, Spanish Courses & Classes in Seattle, MCAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Washington DC

Popular Test Prep

GMAT Test Prep in New York City, ACT Test Prep in Chicago, LSAT Test Prep in Boston, ISEE Test Prep in Phoenix, SAT Test Prep in Phoenix, LSAT Test Prep in Chicago, GRE Test Prep in San Francisco-Bay Area, SSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Atlanta

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 : Adding and Subtracting Rational Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1742 : Algebra Ii

Example Question #81 : Rational Expressions

Example Question #82 : Rational Expressions

Example Question #83 : Rational Expressions

Example Question #84 : Rational Expressions

Example Question #85 : Rational Expressions

Example Question #604 : Intermediate Single Variable Algebra

Example Question #611 : Intermediate Single Variable Algebra

Example Question #88 : Rational Expressions

Example Question #41 : Solving Rational Expressions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: