Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Solving 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 #1821 : Algebra Ii

If $f(x)=\frac{(x+3)}{(x-2)}$ and $g(x)=\frac{(x-2)}{(x+4)}$ , what is f(x)+g(x) ?

Possible Answers:

2x^2 +4x -5

$\frac{x^{2}+7x+12}{x^2+4x-8}$

$\frac{2x^2 -3x+16}{x^2 +2x-8}$

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

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

Correct answer:

$\frac{2x^2 -3x+16}{x^2 +2x-8}$

Explanation:

To begin, let's write the whole problem out plainly:

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

From here, in order to add the two fractions, we need to get the denominators to be the same. To do this, we multiply the numerator and denominator of each fraction by the denominator in the OTHER fraction:

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

Now we can add the fractions together:

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

Now we can expand using FOIL:

$\frac{(x^2+7x+12)+(x^2 -4x+4)}{(x^2+2x-8)}$

Finally, we collect like terms in the numerator for a final answer of:

$f(x)+g(x)=\frac{2x^2-3x+16}{x^2+2x-8}$

Report an Error

Example Question #1822 : Algebra Ii

If $f(x)=\frac{x^2 +3x +8}{x+2}$ , what is f(4) ?

Possible Answers:

$\frac{32}{5}$

$\frac{14}{9}$

Undefined

Correct answer:

Explanation:

First we're going to give the function a quick glance to see if we can simplify by factoring. We can't, so in order to solve, we're going to replace all the 's with the number we want to solve for, :

$f(4)=\frac{(4)^2+3(4)+8}{(4)+2}$

$f(4)=\frac{16+12+8}{4+2}$

$f(4)=\frac{36}{6}$

f(4)=6

Report an Error

Example Question #1823 : Algebra Ii

Solve for x: $\sqrt{x+20}=x$

Possible Answers:

x=-4,-5

x=-4,5

x=4,-5

x=4,5

Correct answer:

x=-4,5

Explanation:

Step 1: We need to square both sides of the equation. Squaring a square root will just leave me with whatever is inside the root.

$(\sqrt{x+20})^2=x^2$

$\rightarrow x+20=x^2$

Step 2: Move all terms on the left side to the right side.

0=x^2-x-20

Step 3: Factor the right side. We want two numbers that multiply to and add to .

$4\cdot-5=-20, 4-5=-1$

Rewrite the trinomial as two binomals:

(x+4)(x-5)=0

Step 4: Set each parentheses equal to and solve for :

(x+4)=0, x=-4
(x-5)=0, x=5

The solutions to this equation are -4 and 5.

Report an Error

Example Question #1824 : Algebra Ii

Solve for .

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

Possible Answers:

Correct answer:

Explanation:

To solve for the variable , isolate the variable on one side of the equation with all other constants on the other side. To accomplish this perform the opposite operation to manipulate the equation.

First cross multiply.

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

Next, divide by four on both sides.

4x=4*3=12

$\frac{4x}{4}=\frac{12}{4}=\frac{4\cdot 3}{4}=3$

x=3

Report an Error

Example Question #1825 : Algebra Ii

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

Possible Answers:

2x+3

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

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

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

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

Correct answer:

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

Explanation:

The terms of the numerator cannot be added or subtracted without a common denominator.

Convert the first term with a denominator of x^2 .

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

Expand the first term and combine the fractions as one fraction. Be sure to enclose the numerator of the second term in parentheses.

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

Simplify this fraction.

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

The answer is: $\frac{x^2+2x-4}{x^2}$

Report an Error

Example Question #1826 : Algebra Ii

Solve for .

$\frac{x}{5}=\frac{7}{10}$

Possible Answers:

2.5

3.5

6.5

Correct answer:

3.5

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{x}{5}=\frac{7}{10}$

Cross multiply.

10x=7*5=35

Divide on both sides.

x=3.5

Report an Error

Example Question #1827 : Algebra Ii

Solve for .

$\frac{2x}{5}=\frac{18}{5}$

Possible Answers:

Correct answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{2x}{5}=\frac{18}{5}$

Cross multiply.

10x=5*18=90

Divide on both sides.

x=9

Report an Error

Example Question #1828 : Algebra Ii

Solve for .

$\frac{3}{4x}=\frac{9}{144}$

Possible Answers:

Correct answer:

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{3}{4x}=\frac{9}{144}$

Cross multiply.

36x=3*144=432

Divide on both sides.

x=12

Report an Error

Example Question #1829 : Algebra Ii

Solve for .

$\frac{x+1}{3}=\frac{7}{2}$

Possible Answers:

9.5

10.5

Correct answer:

9.5

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{x+1}{3}=\frac{7}{2}$

Cross multiply.

2(x+1)=7*3

Remember you are multiplying with the expression. Now distribute.

2x+2=21

Subtract on both sides.

2x=19

Divide on both sides.

x=9.5

Report an Error

Example Question #129 : Solving Rational Expressions

Solve for .

$\frac{x+3}{4}=\frac{7}{16}$

Possible Answers:

2.25

-1.25

1.5625

-1.5625

-1.75

Correct answer:

-1.25

Explanation:

To solve for the variable isolate it on one side of the equation by moving all other constants to the other side. To do this, perform opposite operations to manipulate the equation.

$\frac{x+3}{4}=\frac{7}{16}$

Cross multiply.

16(x+3)=7*4

Remember we are multiplying with the expression. Now distribute.

16x+48=28

Subtract on both sides.

16x=-20

Divide on both sides.

$x=-\frac{5}{4}=-1.25$

Report an Error

View Algebra 2 Tutors

Shruthi
Certified Tutor

Nottingham Trent University, Bachelor of Science, Biomedical Engineering.

View Algebra 2 Tutors

Matthew
Certified Tutor

Bluffton University, Bachelor of Education, Mathematics. Bluffton University, Masters in Education, Education.

View Algebra 2 Tutors

Shivansh
Certified Tutor

University of British Columbia, Bachelor, Math major and data science minor .

All Algebra II Resources

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

Popular Subjects

Reading Tutors in San Francisco-Bay Area, LSAT Tutors in Miami, Chemistry Tutors in Philadelphia, SAT Tutors in San Diego, MCAT Tutors in Philadelphia, Math Tutors in Houston, Computer Science Tutors in Dallas Fort Worth, GMAT Tutors in San Francisco-Bay Area, Spanish Tutors in Phoenix, Calculus Tutors in Los Angeles

Popular Courses & Classes

GRE Courses & Classes in Washington DC, LSAT Courses & Classes in Houston, ISEE Courses & Classes in Atlanta, LSAT Courses & Classes in Boston, ISEE Courses & Classes in San Diego, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in New York City, SAT Courses & Classes in Chicago, LSAT Courses & Classes in Atlanta, ACT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in Washington DC, LSAT Test Prep in San Diego, ISEE Test Prep in Boston, LSAT Test Prep in Atlanta, SAT Test Prep in Seattle, GMAT Test Prep in Seattle, GMAT Test Prep in Denver, LSAT Test Prep in Houston, SAT Test Prep in Atlanta, MCAT Test Prep in Atlanta

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 : Solving Rational Expressions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1821 : Algebra Ii

Example Question #1822 : Algebra Ii

Example Question #1823 : Algebra Ii

Example Question #1824 : Algebra Ii

Example Question #1825 : Algebra Ii

Example Question #1826 : Algebra Ii

Example Question #1827 : Algebra Ii

Example Question #1828 : Algebra Ii

Example Question #1829 : Algebra Ii

Example Question #129 : 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: