Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Adding and Subtracting Rational Expressions: A Math 100/107/111 Tutorial, Study notes of Algebra

University of the Philippines Visayas - Cebu High School (UPVC)Algebra

Instructions and examples for adding and subtracting rational expressions. It covers the process of rewriting fractions with the same denominator, simplifying numerators, and factoring. The tutorial includes practice problems and examples to help students master the concept.

Typology: Study notes

2021/2022

Uploaded on 08/01/2022

hal_s95
hal_s95 🇵🇭

4.4

(655)

10K documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Title: Adding or Subtracting Rational Expressions
Class: Math 100 or Math 107 or Math 111
Author: Lindsey Bramlett-Smith
Instructions to Tutor: Read instructions and follow all steps for each problem exactly as given.
Keywords/Tags: adding rational expressions, subtracting rational expressions, rational expressions
Adding or Subtracting Rational Expressions
Purpose: This is intended to refresh your skills in adding and subtracting rational expressions.
Activity: Work through the following activity and examples. Do all of the practice problems before
consulting with a tutor.
• Adding or subtracting rational expressions is done in the same way as adding or subtracting
fractions. They must have a common denominator.
• Once you have rewritten your fractions so they all have the same denominator, then rewrite as a
single fraction by adding and subtracting the numerators all over the common denominator.
• Once the numerator has been simplified by combining like terms, then, if possible, factor the
numerator (your denominator should be left in factored form) and reduce.
• The rules for simplifying rational expressions are the same as the rules for simplifying fractions:
Only common factors may be reduced.
• It is harder to tell when a rational expression has been factored:
Consider
2
2 15xx−−
=
( ) ( )
25 3xx+−
The last operations are The last operation is the
addition/subtraction. multiplication between the )(.
2
2x
,
x−
, and
15−
( )
25
x+ and
( )
3x−
are
are terms (expressions factors (expressions which
which are added or are multiplied).
subtracted), not factors.
Consider 32
8 4 60xx x
−−
=
42 5 3xx x
3
8x
, 2
4x
−, and
60x−
4, x
,
( )
25
x+, and
( )
3x−
are
are terms. These factors. These can be reduced.
can not be reduced.
Example 1 5 30
66
c
cc
+
++
Example 2 10 5
3737xx
−
−−
5 30
6
c
c
+
+
10 5
37x
−
−
( )
56
6
c
c
+
+
5
37x
−
5
pf3
pf4

Partial preview of the text

Download Adding and Subtracting Rational Expressions: A Math 100/107/111 Tutorial and more Study notes Algebra in PDF only on Docsity!

Title: Adding or Subtracting Rational Expressions Class: Math 100 or Math 107 or Math 111 Author: Lindsey Bramlett-Smith Instructions to Tutor: Read instructions and follow all steps for each problem exactly as given. Keywords/Tags: adding rational expressions, subtracting rational expressions, rational expressions

Adding or Subtracting Rational Expressions

Purpose: This is intended to refresh your skills in adding and subtracting rational expressions.

Activity: Work through the following activity and examples. Do all of the practice problems before consulting with a tutor.

  • Adding or subtracting rational expressions is done in the same way as adding or subtracting fractions. They must have a common denominator.
  • Once you have rewritten your fractions so they all have the same denominator, then rewrite as a single fraction by adding and subtracting the numerators all over the common denominator.
  • Once the numerator has been simplified by combining like terms, then, if possible, factor the numerator (your denominator should be left in factored form) and reduce.
  • The rules for simplifying rational expressions are the same as the rules for simplifying fractions: Only common factors may be reduced.
  • It is harder to tell when a rational expression has been factored :

Consider 2 x^2 − x − 15 = ( 2 x + 5 ) ( x − 3 )

The last operations are The last operation is the addition/subtraction. multiplication between the )(.

2 x^2 , − x , and − 15 ( 2 x + 5 )and ( x − 3 )are

are terms (expressions factors (expressions which which are added or are multiplied). subtracted), not factors.

Consider 8 x^3 − 4 x^2 − 60 x = 4 x ( 2 x + 5 ) ( x − 3 )

8 x^3 , − 4 x^2 , and − 60 x 4, x , ( 2 x + 5 ), and ( x − 3 )are

are terms. These factors. These can be reduced. can not be reduced.

Example 1^5 6 6

c c c

Example 2^10 3 x 7 3 x 7

c c

3 x 7

c c

3 x − 7

5

Practice 1^4 3 3

y y y

Practice 2^3 3 3

y y y

−^ −

Did you get 4? Did you get 1?

  • When terms are being added, we can rewrite their order using the commutative property of addition: 3 + x = x + 3
  • But, subtraction is not commutative: 3 − x ≠ x − 3

• However, we can factor out a − 1 : 3 − x = − 1 ( − 3 + x ) = − 1 ( x − 3 )

So, when you need to rewrite the order of two terms being subtracted, factor out a − 1.

  • Use the following properties to rewrite where you put your negative signs (by convention, we try not to leave any in denominators). A A A B B B

and A^ A^ A^ A B B B B

− = − −^ = − =

Example 3^10 3 x 7 7 3 x

3 x 7 1 3 x 7

3 x 7 3 x 7

3 x − 7

Practice 3^3 3 3

y y y

Did you get –1?

Example 6^5 x 2 x 2

Practice 6^2 x 3 x 3

x x x x x x

x x x x

x x x x

x x x

x x x

Did you get (^ )

x x x

Problems

x x x x x

y y y y y

+ −^ −

x x x x

x x (^) x

+^ −

x 9 x 3

2 2

x x x x

x x x x

( ) (^ )

2

a a a^ a

Review: Meet with a tutor to verify your work on this worksheet and discuss some of the areas that were more challenging for you. If necessary, choose more problems from the homework to practice and discuss with the tutor.

For Tutor Use: Please check the appropriate statement:

Student has completed worksheet but may need further assistance. Recommend a follow-up with the instructor.

Student has mastered topic.