We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : 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 #31 : Systems Of Equations

Simplify:

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

Possible Answers:

$\frac{8x}{x+3}$

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

$\frac{6}{x}$

Correct answer:

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

Explanation:

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

Because the two rational expressions have the same denominator, we can simply add straight across the top. The denominator stays the same.

Therefore the answer is $\frac{6x}{x+3}$ .

Report an Error

Example Question #1 : Solving Rational Expressions

Simplify

$\frac{5}{x^2}-\frac{1}{3x^3}$

Possible Answers:

$\frac{15x-1}{3x^3}$

The expression cannot be simplified.

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

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

$\frac{15x-1}{1}$

Correct answer:

$\frac{15x-1}{3x^3}$

Explanation:

a. Find a common denominator by identifying the Least Common Multiple of both denominators. The LCM of 3 and 1 is 3. The LCM of x^2 and x^3 is x^3 . Therefore, the common denominator is 3x^3 .

b. Write an equivialent fraction to $\frac{5}{x^2}$ using 3x^3 as the denominator. Multiply both the numerator and the denominator by to get $\frac{15x}{3x^3}$ . Notice that the second fraction in the original expression already has 3x^3 as a denominator, so it does not need to be converted.

The expression should now look like: $\frac{15x}{3x^3}-\frac{1}{3x^3}$ .

c. Subtract the numerators, putting the difference over the common denominator.

$\frac{15x-1}{3x^3}$

Report an Error

Example Question #2 : Solving Rational Expressions

Combine the following expression into one fraction:

$\small \frac{x^2+y}{25x}+\frac{z+3}{y}$

Possible Answers:

$\small \frac{25x^3+25xy+yz+3y}{25xy}$

$\small \frac{x^2y+y^2+25xz+75x}{25xy}$

The two fractions cannot be combined as they have different denominators.

$\small \frac{x^2z+yz+3x^2+3y}{25xy}$

$\small \frac{x^2+y+z+3}{25xy}$

Correct answer:

$\small \frac{x^2y+y^2+25xz+75x}{25xy}$

Explanation:

To combine fractions of different denominators, we must first find a common denominator between the two. We can do this by multiplying the first fraction by $\small \frac{y}{y}$ and the second fraction by $\small \frac{25x}{25x}$ . We therefore obtain:

$\small \frac{x^2+y}{25x}\times \frac{y}{y}+\frac{z+3}{y}\times\frac{25x}{25x}$

$\small \small \frac{x^2y+y^2}{25xy}+\frac{25xz+75x}{25xy}$

Since these fractions have the same denominators, we can now combine them, and our final answer is therefore:

$\small \frac{x^2y+y^2+25xz+75x}{25xy}$

Report an Error

Example Question #3 : Solving Rational Expressions

What is $\frac{x+1}{3} + \frac{2x-5}{2}$ ?

Possible Answers:

$\frac{8x-13}{6}$

$\frac{3x-4}{5}$

$\frac{6x-2}{3}$

$\frac{8x+17}{6}$

$\frac{8x+13}{3}$

Correct answer:

$\frac{8x-13}{6}$

Explanation:

We start by adjusting both terms to the same denominator which is 2 x 3 = 6

Then we adjust the numerators by multiplying x+1 by 2 and 2x-5 by 3

$\frac{(x+1)\cdot 2}{3 \cdot 2}+\frac{(2x-5) \cdot 3}{2 \cdot 3}$

The results are:

$\frac{2x+2}{6}+\frac{6x-15}{6}$

So the final answer is,

$\frac{8x-13}{6}$

Report an Error

Example Question #1 : Solving Rational Expressions

What is $\frac{3x-4}{x+2}-\frac{5x+2}{2x+4}$ ?

Possible Answers:

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

$\frac{8x+6}{x+2}$

$\frac{-2x-6}{3x+6}$

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

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

Correct answer:

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

Explanation:

Start by putting both equations at the same denominator.

2x+4 = (x+2) x 2 so we only need to adjust the first term:

$\frac{(3x-4)\cdot 2}{(x+2)\cdot 2}-\frac{5x+2}{2x+4}$

$=\frac{6x-8}{2x+4}-\frac{5x+2}{2x+4}$

Then we subtract the numerators, remembering to distribute the negative sign to all terms of the second fraction's numerator:

$=\frac{6x -8 -5x-2}{2x+4}=\frac{x-10}{2x+4}$

Report an Error

Example Question #1 : Adding And Subtracting Rational Expressions

$\frac{15x+A}{x^{2}+8x+15}=\frac{7}{x+5}+\frac{8}{x+3}$

Determine the value of .

Possible Answers:

Correct answer:

Explanation:

(x+5)(x+3) is the common denominator for this problem making the numerators 7(x+3) and 8(x+5).

7(x+3)+8(x+5)= 7x+21+8x+40= 15x+61

A=61

Report an Error

Example Question #6 : How To Add Polynomials

Add:

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

First factor the denominators which gives us the following:

$\frac{x}{\left ( x+1 \right )\left ( x-3 \right )} + \frac{1}{\left ( x+1 \right )\left ( x-3 \right )}$

The two rational fractions have a common denominator hence they are like "like fractions". Hence we get:

$\frac{x+1}{\left ( x+1 \right )\left ( x-3 \right )}$

Simplifying gives us

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

Report an Error

Example Question #571 : Intermediate Single Variable Algebra

Subtract:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

First let us find a common denominator as follows:

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

Now we can subtract the numerators which gives us : $2x^{2}+2x-3$

So the final answer is $\frac{2x^{2}+2x-3}{\left ( x+1 \right )\left ( x-1 \right )}$

Report an Error

Example Question #4 : How To Find The Solution To A Rational Equation With Lcd

Solve the rational equation:

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

Possible Answers:

$\small x=-2$ or $\small x=2$

$\small x=\frac{1}{5}$

$\small x=1$ or $\small x=5$

$\small x=0$

no solution

Correct answer:

$\small x=1$ or $\small x=5$

Explanation:

With rational equations we must first note the domain, which is all real numbers except $\small \tiny x=2$ . (Recall, the denominator cannot equal zero. Thus, to find the domain set each denominator equal to zero and solve for what the variable cannot be.)

The least common denominator or $\small 2$ and $\small 2x-4$ is $\small 2(x-2)$ . Multiply every term by the LCD to cancel out the denominators. The equation reduces to $\small \small (x-2)(x+2)-3=6(x-2)$ . We can FOIL to expand the equation to $\small \small x^2 -4-3=6x-12$ . Combine like terms and solve: $\small x^2-6x+5=0$ . Factor the quadratic and set each factor equal to zero to obtain the solution, which is $\small x=5$ or $\small x=1$ . These answers are valid because they are in the domain.

Report an Error

Example Question #11 : Solving Rational Expressions

Simplify: 3x-4xy-xy(6x+3)

Possible Answers:

3x+7xy-6x^2y

3x-7xy-6x^2y

3x-12xy-30x^2y

3x-xy-6x^2y

3x+xy-6x^2y

Correct answer:

3x-7xy-6x^2y

Explanation:

First, simplify the expression before attempting to combine like-terms.

3x-4xy-xy(6x+3)

3x-4xy-6x^2y-3xy

Combine like-terms.

3x-7xy-6x^2y

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

Algebra Tutors in New York City, MCAT Tutors in Seattle, LSAT Tutors in Washington DC, Math Tutors in San Francisco-Bay Area, Statistics Tutors in Chicago, Math Tutors in Los Angeles, Biology Tutors in Houston, Algebra Tutors in Philadelphia, GMAT Tutors in Denver, Algebra Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Philadelphia, ACT Courses & Classes in Miami, GMAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Denver, LSAT Courses & Classes in Houston, MCAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Miami, ISEE Courses & Classes in Boston, LSAT Courses & Classes in Atlanta, SSAT Courses & Classes in Phoenix

Popular Test Prep

SAT Test Prep in Phoenix, GRE Test Prep in Houston, GMAT Test Prep in New York City, SSAT Test Prep in New York City, LSAT Test Prep in New York City, ACT Test Prep in Miami, LSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Miami, MCAT Test Prep in New York City, MCAT 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

Algebra II : Rational Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #31 : Systems Of Equations

Example Question #1 : Solving Rational Expressions

Example Question #2 : Solving Rational Expressions

Example Question #3 : Solving Rational Expressions

Example Question #1 : Solving Rational Expressions

Example Question #1 : Adding And Subtracting Rational Expressions

Example Question #6 : How To Add Polynomials

Example Question #571 : Intermediate Single Variable Algebra

Example Question #4 : How To Find The Solution To A Rational Equation With Lcd

Example Question #11 : 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: