We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SSAT Upper Level Math : How to subtract complex fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

Create An Account

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #82 : Fractions

Simplify.

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

Possible Answers:

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

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

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

$\frac{4}{x}$

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

Correct answer:

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

Explanation:

Find the least common denominator which is x^2 .

Just multiply the right fraction top and bottom by .

$\frac{2}{x^2}-\frac{4\cdot x}{x \cdot x}=\frac{2}{x^2}-\frac{4x}{x^2}$

Finally, subtract.

Answer should be,

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

Report an Error

Example Question #2 : How To Subtract Complex Fractions

Simplify.

$\frac{x^2-5x+6}{x^2+2x-8}-\frac{x^2-5x-6}{x^2+x-12}$

Possible Answers:

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

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

$\frac{x-5}{x+4}$

$\frac{-5}{x+4}$

$\frac{5}{x+4}$

Correct answer:

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

Explanation:

Lets try to factor. Remember, we need to find two terms that are factors of the c term that add up to the b term.

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

Next cancel out the like terms.

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

Now combine the numerator. Remember to distribute the negative sign.

This is the final answer:

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

Report an Error

Example Question #3 : How To Subtract Complex Fractions

Simplify.

$1-\frac{3}{x-3}$

Possible Answers:

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

$\frac{x-6}{x-3}$

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

$\frac{1}{x-3}$

Correct answer:

$\frac{x-6}{x-3}$

Explanation:

Turn the into a fraction that has a common denominator with the other fraction. To do this multiply $1 \cdot \frac{x-3}{x-3}$ .

This results in the following expression:

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

With the same denominator, just subtract and remember to distribute the negative sign.

The final answer is

$\frac{x-6}{x-3}$ .

Report an Error

Example Question #4 : How To Subtract Complex Fractions

Solve and simplify.

$\frac{x^2-9}{x+3}-\frac{x^2-16}{x+4}$

Possible Answers:

$\frac{1}{x^2+7x+12}$

$\frac{x^2+7}{x^2+7x+12}$

$\frac{2x}{x^2+7x+12}$

$\frac{7}{x^2+7x+12}$

Correct answer:

Explanation:

Lets try to reduce the fraction. When factoring a difference of squares, the form is (x-a)(x+a) . When you foil, the middle terms cancel out.

So when doing that, we have:

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

Cancel out like terms and we get this:

(x-3)-(x-4) .

Distribute the negative sign and we should get .

Report an Error

Example Question #82 : Rational Numbers

Solve for .

$\frac{1}{\sqrt{x}}-\frac{1}{2\sqrt{x}}=2$

Possible Answers:

${}\frac{1}{4}$

${}\frac{1}{2}$

$\frac{1}{16}$

Correct answer:

$\frac{1}{16}$

Explanation:

First find the least common denominator. That will be $2\sqrt{x}$ .

Multiply top and bottom of the left fraction by .

$\frac{1}{\sqrt{x}}\cdot \frac{2}{2}=\frac{2}{2\sqrt{x}}$

Then subtract the numerator and then cross-multiply to get this:

$\frac{2}{2\sqrt{2}}-\frac{1}{2\sqrt{2}}=2\rightarrow 2-1=2(2\sqrt{x}) \rightarrow 1=4\sqrt{x}$

Then combine like terms. To get rid of the square root,

$\frac{1}{4}=\sqrt{x}$ square both sides to get $\left(\frac{1}{4}\right)^2=\frac{1}{16}$ as the final answer.

Report an Error

Example Question #1 : How To Subtract Complex Fractions

Solve for .

$\frac{5}{x-2}-\frac{2}{x+2}=1$

Possible Answers:

Both and .

Correct answer:

Both and .

Explanation:

Find the least common denominator which is x^2-4 . Then multiply the left fraction numerator by x+2 and multiply the right numerator by x-2 inorder for each fraction to share the common denominator.

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

Distribute and be careful of the negative sign.

$\frac{5x+10-2x+4}{x^2-4}=1$

Cross-multiply and create the quadratic equation.

x^2-3x-18=0

Lets factor. Remember, we need to find two terms that are factors of the c term that add up to the b term.

(x-6)(x+3)=0

x=6 , x=-3

If you check these answers back into the question, none of the fractions are undefined so these are the final answers.

Report an Error

Example Question #7 : How To Subtract Complex Fractions

Solve for .

$\frac{2}{x-1}-\frac{2}{x+1}=\left | 2\right |$

Possible Answers:

$-\sqrt{3}$

$\sqrt{3}$

$\pm\sqrt{3}$

Correct answer:

$\pm\sqrt{3}$

Explanation:

Find the least common denominator which is x^2-1 . Then multiply the left fraction numerator by x+1 and multiply the right numerator by x-1 in order to make each fraction share the common denominator.

$\frac{2(x+1)}{x^2-1}-\frac{2(x-1)}{x^2-1}=\left | 2\right |$

Distribute and be careful of the negative sign.

$\frac{2x+2-2x+2}{x^2-1}=\left | 2\right |$

Simplify the numerator and cross multiply. Because there is an absolute value bar, we need to split this expression into two different equations.

Equation one:

2(x^2-1)=4

2x^2-2=4

2x^2=6

x^2=3

$x=\pm \sqrt{3}$ By inspection, these values pass and don't violate the fractions being undefined.

Equation two:

-2(x^2-1)=4

-2x^2+2=4

-2x^2=2

x^2=-1

x=i This answer is imaginary and not in the choices leaving $\pm \sqrt{3}$ as the answers.

Report an Error

View SSAT- Upper Level Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

View SSAT- Upper Level Tutors

Keith
Certified Tutor

Xavier University, Bachelor in Business Administration, Accounting. Ohio University-Main Campus, Masters in Education, Mathem...

View SSAT- Upper Level Tutors

Carneta
Certified Tutor

Langston University, Bachelor in Arts, Theater Arts.

All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Dallas Fort Worth, English Tutors in San Francisco-Bay Area, SSAT Tutors in Chicago, French Tutors in Houston, Algebra Tutors in Seattle, ACT Tutors in Philadelphia, Physics Tutors in Dallas Fort Worth, Physics Tutors in San Francisco-Bay Area, Chemistry Tutors in Los Angeles, SSAT Tutors in Dallas Fort Worth

Popular Courses & Classes

GRE Courses & Classes in Houston, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC, MCAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Philadelphia, GMAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Washington DC

Popular Test Prep

SAT Test Prep in Los Angeles, SAT Test Prep in Atlanta, ISEE Test Prep in Boston, MCAT Test Prep in Atlanta, ISEE Test Prep in Miami, ACT Test Prep in Philadelphia, GRE Test Prep in Houston, LSAT Test Prep in Washington DC, MCAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Boston

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

SSAT Upper Level Math : How to subtract complex fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #82 : Fractions

Example Question #2 : How To Subtract Complex Fractions

Example Question #3 : How To Subtract Complex Fractions

Example Question #4 : How To Subtract Complex Fractions

Example Question #82 : Rational Numbers

Example Question #1 : How To Subtract Complex Fractions

Example Question #7 : How To Subtract Complex Fractions

All SSAT Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: