We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Intermediate Single-Variable Algebra

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 #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

Example Question #81 : Rational Expressions

Add: $\frac{7}{9x}+\frac{2(4-x)}{x}$

Possible Answers:

$\frac{9x-15}{9x}$

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

$\frac{-18x+79}{9}$

$\frac{9x-79}{9x}$

$\frac{-18x+79}{9x}$

Correct answer:

$\frac{-18x+79}{9x}$

Explanation:

Evaluate by changing the denominator of the second fraction so that both fractions have similar denominators.

$\frac{7}{9x}+\frac{2(4-x)}{x} = \frac{7}{9x}+\frac{2[9](4-x)}{[9]x}$

Use distribution to simplify the numerator.

$\frac{7}{9x}+\frac{2[9](4-x)}{[9]x} =\frac{7}{9x}+\frac{72-18x}{9x}$

Combine like-terms.

The answer is: $\frac{-18x+79}{9x}$

Report an Error

Example Question #51 : Adding And Subtracting Rational Expressions

Add: $\frac{3}{10x}-\frac{10}{x}$

Possible Answers:

$-\frac{7}{10x}$

$-\frac{97}{10}x$

$\frac{7}{10-x}$

$-\frac{7}{10}x$

$-\frac{97}{10x}$

Correct answer:

$-\frac{97}{10x}$

Explanation:

In order to subtract the fractions, we will need to determine the least common denominator.

Multiply the second fraction's numerator and denominator by ten, since both fractions share an x-term.

$\frac{3}{10x}-\frac{10(10)}{x(10)} = \frac{3}{10x}-\frac{100}{10x}$

Combine the numerator to form one fraction.

The answer is: $-\frac{97}{10x}$

Report an Error

Example Question #52 : Adding And Subtracting Rational Expressions

Solve: $\frac{x}{2x-7}+ \frac{7x}{x-7}$

Possible Answers:

$\frac{15x^2-42x}{2x^2-21x+49}$

$\frac{15x-56}{2x^2-21x+49}$

$\frac{14x^2-49x}{2x^2-21x+49}$

$\frac{15x^2-56x}{2x^2-21x+49}$

$\frac{15x}{2x-7}$

Correct answer:

$\frac{15x^2-56x}{2x^2-21x+49}$

Explanation:

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

Use the FOIL method to multiply the two denominators together.

(2x-7)(x-7) = 2x^2-7x-14x+49

Simplify by combining like-terms. The LCD is: 2x^2-21x+49

Change the fractions.

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

Simplify the fractions.

$\frac{x^2-7x}{2x^2-21x+49}+\frac{14x^2-49x}{2x^2-21x+49}$

Combine like-terms.

The answer is: $\frac{15x^2-56x}{2x^2-21x+49}$

Report an Error

Example Question #53 : Adding And Subtracting Rational Expressions

Add: $\frac{3}{2x}+\frac{4}{3x}+\frac{5}{4x}$

Possible Answers:

$\frac{49}{12}x$

$\frac{49}{24x}$

$\frac{14}{3}x$

$\frac{14}{3x}$

$\frac{49}{12x}$

Correct answer:

$\frac{49}{12x}$

Explanation:

Determine the least common denominator in order to add the numerator.

Each denominator shares an term. The least common denominator is since it is divisible by each coefficient of the denominator.

Convert the fractions.

$\frac{3}{2x}+\frac{4}{3x}+\frac{5}{4x} = \frac{3(6)}{2x(6)}+\frac{4(4)}{3x(4)}+\frac{5(3)}{4x(3)}$

Simplify the top and bottom.

$\frac{18}{12x}+\frac{16}{12x}+\frac{15}{12x}=\frac{49}{12x}$

The answer is: $\frac{49}{12x}$

Report an Error

Example Question #54 : Adding And Subtracting Rational Expressions

Solve: $\frac{2}{3x}+\frac{x}{4}-\frac{1}{x}$

Possible Answers:

$\frac{1}{4x}-\frac{1}{3}x$

$\frac{1}{12}x$

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

$\frac{1}{4}x-\frac{1}{3x}$

$\frac{1}{12x}$

Correct answer:

$\frac{1}{4}x-\frac{1}{3x}$

Explanation:

Determine the least common denominator. Each term will need an x-variable, and all three denominators will need a common coefficient.

The least common denominator is 12x .

Convert the fractions.

$\frac{2(4)}{3x(4)}+\frac{x(3x)}{4(3x)}-\frac{1(12)}{x(12)} = \frac{8}{12x}+\frac{3x^2}{12x}-\frac{12}{12x}$

The expression becomes:

$\frac{3x^2-4}{12x} = \frac{x}{4}-\frac{1}{3x}$

The answer is: $\frac{1}{4}x-\frac{1}{3x}$

Report an Error

Example Question #55 : Adding And Subtracting Rational Expressions

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

Possible Answers:

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

$-\frac{x^2+3x+2}{x^2-1}$

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

$-\frac{x^2-3x-2}{x^2-1}$

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

Correct answer:

$-\frac{x^2-3x-2}{x^2-1}$

Explanation:

Notice that x^2-1 can be factorized by the difference of squares. This means that the second fraction will need to multiply the quantity of (x-1) in order for the denominators to be similar.

Convert the fractions.

$\frac{x+3}{x^2-1}-\frac{(x-1)(x-1)}{(x+1)(x-1)}$

Simplify the fractions and combine as one fraction.

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

The expression becomes:

$\frac{x+3-x^2+2x-1}{x^2-1}$

Combine like-terms.

$\frac{-x^2+3x+2}{x^2-1}$

Factor out a negative one from the numerator to pull the negative sign in front of the fraction.

$\frac{-(x^2-3x-2)}{x^2-1}$

The answer is: $-\frac{x^2-3x-2}{x^2-1}$

Report an Error

Example Question #56 : Adding And Subtracting Rational Expressions

For all positive values of x, which of the following expressions is equivalent to the following:

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

Possible Answers:

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

x+6

$\frac{x^2+6x+36}{6x}$

$\frac{x^2+36}{6x}$

$\frac{x^2+5x+6}{6x}$

Correct answer:

$\frac{x^2+6x+36}{6x}$

Explanation:

In order to add the numerators in this expression, we will need to calculate the least common denominator. In this case, the least common denominator is . Let's multiply the fraction on the left by a value of one. Let's start with the left expression. We will multiply it by one in the following form:

$1=\frac{6}{6}$

$\frac{6}{6}\times\frac{6}{x}=\frac{36}{6x}$

Now convert the right fraction to a form with the same denominator. Again, multiply the fraction by a value of one in the following form:

$1=\frac{x}{x}$

$\frac{x}{x}\times\frac{\left(x+6\right)}{6}=\frac{x(x+6))}{6x}$

Now, we can add our two fractions by rewriting them as one whole fraction.

$\frac{36}{6x}+\frac{x(x+6)}{6x}=\frac{36+x(x+6))}{6x}$

Simplify the numerator.

$\frac{36+x(x+6)}{6x} = \frac{36+x^2+6x}{6x}$

$\frac{36+x^2+6x}{6x}= \frac{x^2+6x+36}{6x}$

This cannot be reduced or simplified any further; therefore, the answer is:

$\frac{x^2+6x+36}{6x}$

Report an Error

View Algebra 2 Tutors

Shakeel
Certified Tutor

View Algebra 2 Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Algebra 2 Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ISEE Tutors in San Francisco-Bay Area, Math Tutors in San Francisco-Bay Area, GMAT Tutors in Atlanta, French Tutors in New York City, GRE Tutors in Houston, Reading Tutors in Seattle, English Tutors in San Diego, Calculus Tutors in Los Angeles, SAT Tutors in Dallas Fort Worth, French Tutors in Dallas Fort Worth

Popular Courses & Classes

LSAT Courses & Classes in Houston, ISEE Courses & Classes in New York City, ACT Courses & Classes in Houston, ACT Courses & Classes in New York City, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Houston, ISEE Courses & Classes in Los Angeles, ACT Courses & Classes in Seattle, LSAT Courses & Classes in Phoenix, SAT Courses & Classes in Chicago

Popular Test Prep

SAT Test Prep in Denver, ACT Test Prep in Seattle, GRE Test Prep in Philadelphia, ACT Test Prep in New York City, ISEE Test Prep in Seattle, GRE Test Prep in Denver, ACT Test Prep in Washington DC, SSAT Test Prep in New York City, SAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver

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 : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #611 : Intermediate Single Variable Algebra

Example Question #88 : Rational Expressions

Example Question #41 : Solving Rational Expressions

Example Question #81 : Rational Expressions

Example Question #51 : Adding And Subtracting Rational Expressions

Example Question #52 : Adding And Subtracting Rational Expressions

Example Question #53 : Adding And Subtracting Rational Expressions

Example Question #54 : Adding And Subtracting Rational Expressions

Example Question #55 : Adding And Subtracting Rational Expressions

Example Question #56 : Adding And Subtracting Rational Expressions

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: