We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Algebra : Rational Expressions: CCSS.Math.Content.HSA-APR.D.7

Study concepts, example questions & explanations for Common Core: High School - Algebra

Create An Account

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Rational Expressions: Ccss.Math.Content.Hsa Apr.D.7

Simplify:

$\frac{x - 19}{x - 16} + \frac{x + 1}{x - 5}$

Possible Answers:

$\frac{x^{2} + 16 x}{x - 5}$

$\frac{2 x - 18}{2 x - 21}$

$\frac{2 x + 20}{2 x - 21}$

$\frac{ 2 x^{2} - 39 x + 79 }{ x^{2} - 21 x + 80 }$

$\frac{ 2 x^{2} - 6 x + 79 }{ x^{2} - 21 x + 80 }$

Correct answer:

$\frac{ 2 x^{2} - 39 x + 79 }{ x^{2} - 21 x + 80 }$

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.

$\frac{\left( x + 1 \right) \left( x - 16 \right)}{\left( x - 5 \right) \left( x - 16 \right)}+ \frac{\left( x - 19 \right) \left( x - 5 \right)}{\left( x - 5 \right) \left( x - 16 \right)}$
Now we can use FOIL for the numerator and the denominator.

$=\frac{ x^{2} - 15 x - 16 }{ x^{2} - 21 x + 80 }+ \frac{ x^{2} - 24 x + 95 }{ x^{2} - 21 x + 80 }$
Now we can combine the fractions since they have a common denominator, and put the like terms together.

$=\frac{ x^{2} - 15 x - 16 + x^{2} - 24 x + 95 }{ x^{2} - 21 x + 80 }$

$=\frac{ 2 x^{2} - 39 x + 79 }{ x^{2} - 21 x + 80 }$

Report an Error

Example Question #331 : Arithmetic With Polynomials & Rational Expressions

Simplify:

$\frac{x}{x - 17} + \frac{x - 10}{x - 3}$

Possible Answers:

$\frac{ 2 x^{2} + 7 x + 170 }{ x^{2} - 20 x + 51 }$

$\frac{ 2 x^{2} - 30 x + 170 }{ x^{2} - 20 x + 51 }$

$\frac{x^{2} + 17 x}{x - 3}$

$\frac{2 x - 10}{2 x - 20}$

Correct answer:

$\frac{ 2 x^{2} - 30 x + 170 }{ x^{2} - 20 x + 51 }$

Explanation:

The first step we need to take in order to simplify this expression is to find a common denominator.

We do this by multiplying by a clever form of one to each fraction.

$\frac{\left( x - 10 \right) \left( x - 17 \right)}{\left( x - 3 \right) \left( x - 17 \right)}+ \frac{\left( x \right) \left( x - 3 \right)}{\left( x - 3 \right) \left( x - 17 \right)}$
Now we can use FOIL for the numerator and the denominator.

$=\frac{ x^{2} - 27 x + 170 }{ x^{2} - 20 x + 51 }+ \frac{ x^{2} - 3 x }{ x^{2} - 20 x + 51 }$
Now we can combine the fractions since they have a common denominator, and put the like terms together.

$=\frac{ x^{2} - 27 x + 170 + x^{2} - 3 x }{ x^{2} - 20 x + 51 }$

= $\frac{ 2 x^{2} - 30 x + 170 }{ x^{2} - 20 x + 51 }$

Report an Error

View Tutors

Joshua
Certified Tutor

Murray State University, Bachelor in Arts, Spanish. Lipscomb University, Bachelor of Science, Teacher Assistant.

View Tutors

Kaylee
Certified Tutor

Brigham Young University, Bachelor, MFA - Animation.

View Tutors

Lydia
Certified Tutor

The Richard Stockton College of New Jersey, Bachelor of Science, Biochemistry and Molecular Biology.

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Philadelphia, GMAT Tutors in Houston, Algebra Tutors in Philadelphia, Math Tutors in Houston, English Tutors in Chicago, Physics Tutors in Denver, MCAT Tutors in Miami, Algebra Tutors in New York City, Physics Tutors in Phoenix, ACT Tutors in Houston

Popular Courses & Classes

GRE Courses & Classes in Miami, MCAT Courses & Classes in San Diego, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Houston, SAT Courses & Classes in Houston, SAT Courses & Classes in Boston, GRE Courses & Classes in Los Angeles, Spanish Courses & Classes in Miami, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in Denver

Popular Test Prep

GMAT Test Prep in Houston, SAT Test Prep in Philadelphia, ACT Test Prep in Washington DC, SAT Test Prep in Houston, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Philadelphia, ISEE Test Prep in Phoenix, MCAT Test Prep in Seattle, LSAT Test Prep in New York City, SSAT Test Prep in San Diego

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

Common Core: High School - Algebra : Rational Expressions: CCSS.Math.Content.HSA-APR.D.7

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #11 : Rational Expressions: Ccss.Math.Content.Hsa Apr.D.7

Example Question #331 : Arithmetic With Polynomials & Rational Expressions

All Common Core: High School - Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: