GRE Math : How to find excluded values

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 #10 : How To Find Excluded Values

Which of the following are answers to the equation below?

$\frac{x^2-4}{x^2+5x+6}=0$

I. -3

II. -2

III. 2

Possible Answers:

III only

II only

I, II, and III

I only

II and III

Correct answer:

III only

Explanation:

Given a fractional algebraic equation with variables in the numerator and denominator of one side and the other side equal to zero, we rely on a simple concept. Zero divided by anything equals zero. That means we can focus in on what values make the numerator (the top part of the fraction) zero, or in other words,

x^2-4=0

The expression x^2-4 is a difference of squares that can be factored as

(x-2)(x+2)=0

Solving this for gives either or . That means either of these values will make our numerator equal zero. We might be tempted to conclude that both are valid answers. However, our statement earlier that zero divided by anything is zero has one caveat. We can never divide by zero itself. That means that any values that make our denominator zero must be rejected. Therefore we must also look at the denominator.

x^2+5x+6=0

The left side factors as follows

(x+3)(x+2)=0

This means that if is or , we end up dividing by zero. That means that cannot be a valid solution, leaving as the only valid answer. Therefore only #3 is correct.

Report an Error

Example Question #1 : How To Find Excluded Values

Which of the following provides the complete solution set for |2-z|>0 ?

Possible Answers:

z>2

z=2

$\dpi{100} z|z\neq 2$

z<2

No solutions

Correct answer:

$\dpi{100} z|z\neq 2$

Explanation:

The absolute value will always be positive or 0, therefore all values of z will create a true statement as long as $2-z\neq 0$ . Thus all values except for 2 will work.

Report an Error

Example Question #1 : Algebraic Fractions

If $f(x)=\frac{(x^2-25)}{(3x^2+4x-7)}$ then which values of cannot exist?

Possible Answers:

x=-7

x=-1

x=1

x=-5

x=5

Correct answer:

x=1

Explanation:

The denominator of a fraction can never be equal to 0.

Therefore, to find out what x cannot be equal to, we must factor the denominator, and determine what values of x would make it equal to 0.

3x^2+4x-7=(3x+7)(x-1)

Therefore, $x\neq-\frac{7}{3}$ and $x\neq1$ .

Report an Error

Example Question #1 : Algebraic Fractions

If $f(x)=\sqrt{x^2-16}$ then which cannot be an value?

Possible Answers:

x=-5.2

x=16

x=4

x=-6.7

x=3.5

Correct answer:

x=3.5

Explanation:

You cannot take the square root of a negative number.

Setting up the inequality we get:

$x^2-16\ge 0$

Solving for we get:

$x^2\ge 16$

$x\ge \sqrt{16}$

$x\ge 4$

Therefore any value less than four will not work, x=3.5 .

Another approach is to plug in each of the possible values.

When plugged into $f(x)=\sqrt{x^2-16}$ all of the answers give us a value greater than or equal to 0, except for x=3.5 , which gives us $\sqrt{-3.75}$ .

Report an Error

Example Question #1 : How To Find Excluded Values

Find the excluded values of the following algebraic fraction

$\frac{2x^2-5x-12}{x^2-11x+28}$

Possible Answers:

$x\neq7$

$x\neq4$

$x\neq4,7$

The numerator cancels all the binomials in the denomniator so ther are no excluded values.

$x\neq-11$

Correct answer:

$x\neq4,7$

Explanation:

To find the excluded values of a algebraic fraction you need to find when the denominator is zero. To find when the denominator is zero you need to factor it. This denominator factors into

(x-7)(x-4)

so this is zero when x=4,7 so our answer is

$x\neq4,7$

Report an Error

All GRE Math Resources

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

Popular Subjects

GMAT Tutors in Philadelphia, Reading Tutors in Chicago, Physics Tutors in Los Angeles, MCAT Tutors in San Francisco-Bay Area, English Tutors in San Francisco-Bay Area, ISEE Tutors in New York City, French Tutors in San Francisco-Bay Area, Spanish Tutors in San Diego, GRE Tutors in Atlanta, Biology Tutors in Atlanta

Popular Courses & Classes

Spanish Courses & Classes in Seattle, ISEE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Denver, ACT Courses & Classes in Boston, ISEE Courses & Classes in Philadelphia, LSAT Courses & Classes in Denver, ISEE Courses & Classes in Chicago, SAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in New York City

Popular Test Prep

GMAT Test Prep in San Diego, LSAT Test Prep in Denver, ISEE Test Prep in New York City, SAT Test Prep in Atlanta, ISEE Test Prep in Boston, ACT Test Prep in Philadelphia, SAT Test Prep in New York City, LSAT Test Prep in Houston, ACT Test Prep in Houston, SSAT Test Prep in San Francisco-Bay Area

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 find excluded values

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #10 : How To Find Excluded Values

Example Question #1 : How To Find Excluded Values

Example Question #1 : Algebraic Fractions

Example Question #1 : Algebraic Fractions

Example Question #1 : How To Find Excluded Values

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details