Mathematics

Quarter 1 – Module 4
Simplifying Rational Algebraic
Expressions
Mathematics – Grade 8
Alternative Delivery Mode
Quarter 1 – Module 4 Simplifying Rational Algebraic Expressions
First Edition, 2020

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Published by the Department of Education

Secretary: Leonor Magtolis Briones
Undersecretary: Diosdado M. San Antonio

Development Team of the Module

Author: Vincent Butch S. Embolode, Genevieve B. Estal

Content Evaluator: Reechen Mae A. Piamonte
Language Editor: Merjorie A. Dalagan
Reviewers: Nilo B. Montaño, Lilibeth S. Apat, Liwayway J. Lubang, Rhodora C. Luga, Lee C. Apas,
Jenny O. Pendica, Emmanuel S. Saga
Illustrator: Genevieve B. Estal
Layout Evaluator: Jake D. Fraga
Management Team: Francis Cesar B. Bringas
Isidro M. Biol, Jr.
Rhea J. Yparraguirre
Maripaz F. Magno
Josephine Chonie M. Obseñares
Josita B. Carmen
Celsa A. Casa
Regina Euann A. Puerto
Bryan L. Arreo
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Leopardo P. Cortes

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 8

Mathematics
Quarter 1 – Module 4
Simplifying Rational Algebraic
Expressions
Introductory Message
For the facilitator:

Welcome to the Mathematics 8 Alternative Delivery Mode (ADM) Module on Simplifying

Rational Algebraic Expressions!
This module was collaboratively designed, developed and reviewed by educators both
from public and private institutions to assist you, the teacher or facilitator in helping the
learners meet the standards set by the K to 12 Curriculum while overcoming their
personal, social, and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration their
needs and circumstances.

As a facilitator, you are expected to orient the learners on how to use this module. You
also need to keep track of the learners' progress while allowing them to manage their
own learning. Furthermore, you are expected to encourage and assist the learners as
they do the tasks included in the module.

For the learner:

Welcome to the Mathematics 8 Alternative Delivery Mode (ADM) Module on Simplifying
Rational Algebraic Expressions!

This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning resource while being an active learner.

ii
This module has the following parts and corresponding icons:

This will give you an idea of the skills or

What I Need to Know competencies you are expected to learn in
the module.
This part includes an activity that aims to
What I Know check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
This is a brief drill or review to help you link
What’s In the current lesson with the previous one.
In this portion, the new lesson will be
What’s New introduced to you in various ways; a story, a
song, a poem, a problem opener, an activity
or a situation.
This section provides a brief discussion of the
What is It lesson. This aims to help you discover and
understand new concepts and skills.
This comprises activities for independent
What’s More practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the
end of the module.
This includes questions or blank
What I Have Learned sentence/paragraph to be filled in to process
what you learned from the lesson.
This section provides an activity which will
What I Can Do help you transfer your new knowledge or skill
into real life situations or concerns.
This is a task which aims to evaluate your
Assessment level of mastery in achieving the learning
competency.
In this portion, another activity will be given to
Additional Activities you to enrich your knowledge or skill of the
lesson learned.
This contains answers to all activities in the
Answer Key module.

iii
At the end of this module you will also find:

References This is a list of all sources used in developing

this module.

The following are some reminders in using this module:

1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not hesitate to
consult your teacher or facilitator. Always bear in mind that you are not alone.
We hope that through this material, you will experience meaningful learning and gain
deep understanding of the relevant competencies. You can do it!

iv
 What I Need to Know

This module was designed and written for you to answer the activity you’ve missed
while you are away from school. It is here to help you simplify rational algebraic
expressions. The scope of this module permits it to be used in many different learning
situations. The language used recognizes your diversity and diverse vocabulary level.
The lessons are arranged to follow the standard sequence of the course. But the order
in which you read them can be changed to correspond with the textbook you are now
using.

This module contains:

Lesson 1: Simplifying Rational Algebraic Expressions

After going through this module, you are expected to:

1. identify if the given algebraic expression is in simplest form;

2. express rational algebraic expressions in simplest form; and
3. appreciate the application of rational algebraic expression in real-life situations

1
 What I Know

PRE-ASSESSMENT

Choose the letter of the correct answer and write it on your answer sheet.

1. When is a rational algebraic expression in lowest term?

A. If the numerator and denominator are both of degree one.

B. If either the numerator or the denominator is factored completely.
C. If the numerator and denominator have no common factor other than 1.
D. If the numerator and denominator have no common factor other than −1.

2. Which of the following is one of the steps in simplifying rational expressions?

A. Add the common factors.
B. Subtract out the common factors.
C. Multiply the common factors.
D. Divide out the common factors.

3. Which of the following is the simplified form of the rational expression 𝑥+5 ?
5+𝑥

A. – 1 B. 1
𝑥+5
C. 2 D. 5+𝑥

𝑥 −1
2

1−2𝑥+𝑥2
4. In the rational algebraic expression
, what factor is common to both numerator and

A. 𝑥 + 1 C. 𝑥2 − 1
denominator?

B. 𝑥 − 1 D. 𝑥2 + 1
𝑥 +2𝑥+1
2
5. Which of the following is the simplest form of

𝑥2−1
?
C. 𝑥+1
1−𝑥
A. 𝑥+1
𝑥−1 𝑥−1
B. 𝑥+1 D. 𝑥+1
1−𝑥

𝑥+1
6. Which of the following rational expression has
A. 2𝑥+1
2 as simplest form?

B. 𝑥2−1 𝑥2+2𝑥+1
4

2𝑥+2 C. 2𝑥+2
(𝑥+1)(𝑥+2)
D. 2𝑥+2

2𝑎 𝑏 𝑐
2 3 4 2
�
7. Which of the following is the simplest form of �
2

4𝑎4𝑏𝑐4
?
𝑎
2
A. 2𝑏
2

𝑏
2
B.
2
 𝑎
2𝑏2𝑐4
2
C.
𝑏
2𝑎2𝑐4
2
D.

3
 𝑦
2
−1

𝑦3−1
8. Which of the following is the simplest form of ?

𝑦+1
𝑦
A. 1
C. 𝑦2+𝑦+1
𝑦−1 𝑦+1
1
B.
D. 𝑦2−𝑦+1
𝑎
2
−1
9. Which of the following is the simplest form of ?
1−𝑎2
A. 0 C. −1
B. 1 D. 2
2
+7𝑥+3

2𝑥2−5𝑥−3
2𝑥
10. Which of the following is the simplest form of ?

A. 7𝑥

𝑥+7
−5𝑥

𝑥−5
2𝑥+3
C.
2𝑥−3
B.
𝑥+3
𝑥−3
11. (𝑥−1) 𝑥 (𝑥+1)
2 D.
−1

(𝑥+1)( 𝑥−1)
Given= =

𝑥(𝑥−1)
= 1. Is the process of simplifying the rational
𝑥2−𝑥 = 𝑥(𝑥−1)
1
1
expression correct?
A. Yes, because 𝑥
2
−1
is equivalent to 1 which is equal to1.
𝑥2−𝑥 1
B. Yes, because the process followed the steps in simplifying rational expression.
C. No, because dividing out of the common factors were done incorrectly.
D. No, because the factors of the numerator and denominator are incorrect.

12. Suppose you are painting a square whose side measures 𝑠 long. What is the ratio of
the perimeter to the area of the wall in simplest form?
A. 2
𝑠
C. 4

𝑠
B. 2 4

𝑠
D.

13. Suppose the city circle has a radius 𝑟. What is the ratio of the circumference to the area of
2

the city circle in simplest form?

C. 𝑟
A. 1
2

𝑟
2
B.
D.
𝑟2
2𝑟

𝑥+2
𝑥 −4𝑥+4 in
14. Is the rational expression 2
simplest form?

A. Yes, because the numerator and the denominator have no common factor other than
1.
B. Yes, because the numerator and the denominator are in simplest form of a
polynomial expression.
C. No, because the numerator and the denominator have different degrees.
D. No, because the numerator and the denominator were not factored completely.

1
15. Is the rational expression 𝑥−9 in simplest form?
9−𝑥
A. Yes, because the numerator and the denominator are in simplest form of a
polynomial expression.
B. Yes, because the numerator and the denominator are both polynomial expression.
C. No, because negative one can still be factored from either the numerator or the
denominator.
D. No, because negative one can still be factored from both the numerator and the
denominator.

5
 Lesson
Simplifying Rational
1 Algebraic Expressions

Recall that a rational number is a number that can be written as one integer divided by
another integer, such as 1 ÷ 2 or 1. We usually use the word fraction to mean 1. This idea can be
2 2

polynomial, such as (𝑥 + 1) ÷ (2𝑥 + 3) or 𝑥+1 .

extended to algebraic expression. A rational expression is a polynomial divided by another

2𝑥+3

In your previous grade level, you learned the concept of similar fractions, equivalent
fractions, and simplifying fractions.
15 3
For example, you know that a fraction is equivalent to and can be simplified in the

following manner: 20 4

15 3∙ 3 3
= ∙ 1
5 =
= 4 4
20 4 ∙ 5

Let us review your knowledge in reducing fractions to its simplest form by performing the
activity below.

What’s In

Activity 1: Plain and Simplest

Match the given fractions in column A to its simplest form in column B. Write your answer
on a separate sheet of paper.
A B
7 1
1. A.
28 2
2 4
2. B.
4 5
7
10 C.
3. 25 9
7
14 D.
4. 18 3
1
28 E.
5. 12 4
2
F.
5

6
 Questions:

1. What did you do to reduce each fraction to its simplest form?

2. When can you say that a fraction is already in its simplest form?

Just like rational numbers, rational algebraic expressions can also be expressed in its
simplest form. The next activity will utilize your knowledge in factoring polynomials.

What’s New

Let Go and Be Unique!

Complete the table below. In each item, a pair of polynomial is given. The third column is
the factored form of each polynomial, the fourth column or the Let Go column is the factor/s
common to each pair of polynomials, and the last column or the Be Unique column is the
factor/s not common to each pair of polynomials. Write your answer on a separate sheet of
paper. The first item is done to serve as an example, you may start in the second item.

Item
Given Factored Form Let Go Be Unique

𝑥2 + 𝑥 − 6 𝑥−2
No.

𝑥+3
𝑥2 − 9 𝑥−3
(𝑥 − 2)(𝑥 + 3)
1.
(𝑥 − 3)(𝑥 + 3)

12𝑎2𝑏
15𝑎
2.

3𝑥2 − 12𝑥
3.

𝑥2 + 4𝑥 + 3
6𝑥2 + 3𝑥

𝑥2 − 3𝑥 − 4
4.

𝑥2 + 6𝑥 + 5
2𝑥2 + 11𝑥 + 5
5.

Guide Questions:

1. What techniques did you use to identify the factors of the given polynomials?
2. If you are going to write the remaining factors in the Be Unique column as rational
expressions, are these rational expressions in simplest form? Why or why not?

7
 What is It

A fraction is said to be in simplified form when all pair of factors common to the
numerator and denominator have been removed.

To simplify a fraction, we remove a factor equal to 1. This can be done in two ways. For
9
example, to simplify , we proceed as follows:
15

Method 1 Method 2
9 3∙ Factor the numerator 9 3∙ Factor the numerator and
= =
15 3 and the denominator 15 3 the denominator
5∙ 5∙
3 3

3 3 𝑎∙𝑐 = 𝑎 ∙ 𝑐;
1
3 ∙ Divide out common factor
∙
𝑏∙𝑐 𝑏 𝑐
= 5 3 Separate = 3 1
and divide out
5∙
common factors
3

= 3 Any number, except = 3∙ Multiply numerator by

∙
1 0, divided by itself 1 numerator and
5 is equal to 1. 5∙ denominator by
1 denominator
3 Identity Property of 3 Identity Property of
= =
5 Multiplication 5 Multiplication

Similarly, a rational expression is said to be in simplified form when its numerator and
denominator have no common factor other than 1.

The process of simplifying rational algebraic expressions is similar to simplifying

fractions. That is, we write the rational algebraic expressions so that the numerator and
denominator have no common factors other than 1.

Steps on Simplifying Rational Expression

1. Factor completely the numerator and denominator.

2. Separate and divide out common factor/s if there is/are any.

3. Multiply the remaining factors.

8
Examples
3
1. Write the rational expression 28𝑥 in simplest form.
7𝑥4

28𝑥3 4(7𝑥3)
𝑥(7𝑥3)
= Factor completely the numerator and denominator.
7𝑥4
3
= Separate and divide out common factors.
𝑥 ∙ 7𝑥3
4 7𝑥

𝑥
4
= ∙1 Multiplying the remaining factors.

𝑥
4
=
3
Thus, 4 is the simplest form of 28𝑥
.
𝑥 7𝑥4

2. Write the rational expression 3𝑥−12

5𝑥−20 in simplest form.

3𝑥−12 3 (𝑥−4)
5𝑥−20 5 (𝑥−4)
= Factor completely the numerator and denominator.

𝑥−4
∙𝑥−4
= 3 Separate and divide out common factors.
5

3
= ∙1 Multiplying the remaining factors.
5

3
= 5

3𝑥−12
Thus, 3 is the simplest form of
5𝑥−20
.
5

𝑥
2
+
𝑥𝑦+𝑦
3. Express
2 in simplest form.
𝑥3−𝑦3

𝑥2+ 𝑥2+ 𝑥𝑦+𝑦2 Factor completely the numerator and

𝑥𝑦+𝑦2 (𝑥−𝑦)(𝑥2+
=
denominator.
𝑥3−𝑦3 𝑥𝑦+𝑦2)

𝑥 + 𝑥𝑦+𝑦
2 2

𝑥−𝑦∙ 𝑥2+ 𝑥𝑦+𝑦2

= 1 Separate and divide out common factors.

𝑥−𝑦
1
= ∙1 Multiplying the remaining factors.

𝑥−𝑦
1
=

𝑥 +
2
𝑥𝑦+𝑦2
𝑥−𝑦
1
Thus,
𝑥3−𝑦3
is the simplest form of .

9
 𝑝
3
+ 𝑞3

𝑝2 − 𝑞2
4. Simplify .

𝑝3+ 𝑞3 ( 𝑝+𝑞 )(𝑝2−𝑝𝑞+ Factor completely the numerator and

𝑝2 − 𝑞2 𝑞2) ( 𝑝+𝑞)
=
denominator.
( 𝑝−𝑞)

𝑝2−𝑝𝑞+ 𝑞2 𝑝+𝑞
𝑝−𝑞 𝑝∙
+𝑞
= Separate and divide out common factors.

𝑝2−𝑝𝑞+ 𝑞2
𝑝−𝑞
= ∙1 Multiplying the remaining factors.

𝑝2−𝑝𝑞+ 𝑞2
𝑝−𝑞
=

𝑝 −𝑝𝑞+ 𝑞2 − 𝑞3
is the simplest form of 𝑝
2 3
Thus, .
𝑝−𝑞 𝑝2 − 𝑞2

In some instance, you may encounter certain situations where a factor in the numerator
is in opposite sign of a factor in the denominator. To proceed with this kind of problem, factor
out negative one (−1) or a negative number so that the factors will become equivalent.

Examples:

1. Express
𝑥−𝑦
in simplest form.
𝑦−𝑥

𝑥−𝑦 𝑥−𝑦 Factor completely the numerator and denominator (by

𝑦−𝑥 = −1(𝑥−𝑦) factoring −1 in the denominator).

𝑥−𝑦
−1 ∙𝑥−𝑦
= 1 Separate and divide out common factors.

1
= ∙1 Multiplying the remaining factors.
−1

= −1
𝑥−𝑦
𝑦−𝑥
Thus, −1 is the simplest form of .

3𝑥−9
2. Simplify .
12−4𝑥

3𝑥−9 3(𝑥−3) Factor completely the numerator and denominator (by

12−4𝑥
= −4(𝑥−3) factoring −4 in the denominator).

𝑥−3
−4 ∙𝑥−3
= 3 Separate and divide out common factors.

3
= ∙1 Multiplying the remaining factors.
−4

= 3
−4
3𝑥−9
3
Thus, − is the simplest form of .
4 12−4𝑥

10
 𝑥
2
+5𝑥−14

4 − 𝑥2
3. Write in lowest terms.

𝑥2+5𝑥−1 𝑥2+5𝑥−14
= Factor out −1 in the denominator.
44 −1(𝑥2−4)
− 𝑥2
(𝑥−2)(𝑥+7) Factor completely the numerator and
−1(𝑥−2)(𝑥+2) denominator
𝑥+7 𝑥−2
−1(𝑥+2)
∙ 𝑥−2
= Separate and divide out common factors.

𝑥+7
−1(𝑥+2)∙
= 1 Multiplying the remaining factors.

𝑥+7
− 𝑥+2
=
𝑥+7 𝑥
2
+5𝑥−14
Thus, − is the simplest form of .
𝑥+2 4 − 𝑥2

such that a ≠ 0, the rational expression 𝑎 over the

𝑎
Note that given the expression −𝑎
opposite of 𝑎 is equal to negative one. That is, 𝑎 = −1.
−𝑎

What’s More

Activity 1: Simplest, or Not Simplest, that is the Question

Identify if the given rational expression is in simplest form or not. Write S if the given is in
simplest form otherwise write NS. Write your answer on a separate sheet of paper.
1. 8𝑏2

3𝑎−𝑏2
4𝑎𝑏 6. 3𝑏2−𝑎
𝑥+4
4+ 𝑥 7. −(𝑥+4)
2.
𝑥−4
3. 2𝑥+4
𝑥+2 2𝑥+3
−(3+2𝑥)
8.
𝑥
𝑥+2 𝑥+2
4.
2𝑥+2
9.
𝑥2+4𝑥+3
𝑥2+6𝑥+8 𝑚2−𝑛2
5.
𝑚3+𝑛3
10.
Activity 2: The Simplest of Them All

Express the given algebraic expression to its simplest form. Write your answer on a
separate sheet of paper.
1. 45𝑎2𝑏
30𝑎𝑏 4. 4𝑥2−9
4𝑎−1
8𝑥3−27
2.

2𝑎2+4𝑎−6
1−4𝑎 5. 2𝑎2−2

𝑥2−3𝑥−10
3. 12𝑎2−2
𝑥2−7𝑥+10
1𝑎 6.
12𝑎2−2
8𝑎

11
 𝑥2−2𝑥−
2𝑥2+𝑥−21
15−2𝑥− 2𝑥2−3𝑥−9
7.
3 9.

𝑥2
−𝑥2+𝑥+
(𝑥2+𝑥𝑦+𝑦2)
(𝑥2−𝑦2)

(𝑥3−𝑦3)(𝑥+𝑦)
8.
10.
𝑥2−3𝑥+
2
2

What I Have Learned

What a Wonderful Week

Reflect on the topic and activities you have done this week by completing the following
statements. Write your answers on a separate sheet of paper.

 This week, I learned about .

 To reduce a rational algebraic expression to simplest form, there are steps to follow. First
, then , and lastly .
𝑥
2
+𝑥−2

𝑥2+2𝑥− 3
 For instance, in reducing , it should be written as:

𝑥2 + 𝑥 − 2
𝑥2 + 2𝑥 −
=
3
=
=
 It is also possible to encounter a certain case where a factor in the numerator is in opposite
sign of a factor in the denominator. In this situation, I need to factor
so that the factors will be equivalent.
2
−8𝑥
 Just like in solving 2𝑥 , , it should be written as
12−3𝑥

2𝑥2 −
=
8𝑥
12 − 3𝑥
=
=
=

 In general, given an expression 𝑎 ≠ 0, the rational expression 𝑎 over the opposite of 𝑎 is equal
to that is, 𝑎 = .
−𝑎

 Finally, I can say that a rational expression is in simplest form when its numerator and
denominator have .

2
 What I can Do

Unboxing

thin rectangular shoe box with square base which has a volume 𝑉 = 𝑠2ℎ and a surface area 𝑆𝐴
Vince’ s parents bought him a new pair of school shoes. The shoes was placed in an ultra-

2𝑠2 + 4𝑠ℎ.
=

Express the ratio of the volume to its surface area ( 𝑉 ) in simplest form. Write your answer
𝑆𝐴
on a separate sheet of paper.

11
 Assessment

Choose the letter of the correct answer and write it on your answer sheet.

1. Which of the following fractions is expressed in simplified form?

2
A.
3 C. 13
39
4
B. 7
1 D.
2 42

2. Which of the following is the correct order of simplifying rational algebraic expressions?
I. Multiply the remaining factors.
II. Factor completely the numerator and denominator.
III. Separate and divide out common factor/s if there is/are any.

A. 1, II, III C. II, III, I

B. I, III, II D. III, II, I

3. Which of the following is a rational expression in simplest form?

C. 𝑎2−1
A. 2𝑦
𝑎3+1
4𝑥
B. 2𝑥−
D. 2𝑎2+7𝑎−4
𝑎+2
6
34

𝑥−7
4. Which of the following is equivalent to the rational expression 7−𝑥 ?

A. -1 C. -1 and 1
B. 1 D. Neither -1 nor 1
2
8𝑥𝑦
5. Which of the following is the simplest form of

12𝑥2𝑦
?
C. 4𝑦
𝑥
A. 2𝑦
3𝑥
B. 2𝑥
D. 𝑦
4𝑥
3𝑦

𝑥 −2𝑥 +𝑥
3 2

𝑥3−𝑥
6. Which of the following is the simplest form of ?

A. 𝑥+1
𝑥−1
𝑥+1
C. 1−𝑥
B. 𝑥+ D. 𝑥−1
𝑥+1
1

𝑥
1−

12
 𝑥 −1
2

𝑥3−1
7. Which of the following is the simplest form of ?

𝑥+1
A𝑥−1.
1
C. 𝑥2−𝑥+1
𝑥+1
B. 𝑥2+𝑥+1 𝑥+1
1
D.

8. Which of the following rational expression has −1 as simplest form?

A. 𝑥+1
𝑥−1
𝑥−1
C. 1−𝑥
B. −𝑥+1
D. 𝑥−1
𝑥−1
1−𝑥

𝑥
3
−1
9. Which of the following is the simplest form of ?
1−𝑥3

A. 3 C. 1
B. −3 D. −1
2
+5𝑥+1

6𝑥2−𝑥−1
6𝑥
10. Which of the following is the simplest form of ?

A. 3𝑥+1
2𝑥−1 C. 2𝑥+1
3𝑥−1
B. 3𝑥+
D. 2𝑥+1
3𝑥− 2𝑥−1
1

(𝑥+1)(𝑥−1)
11. Given 𝑥 = (𝑥+1)(𝑥−1) = (𝑥+1)(𝑥−1)
2
−1
=1 ∙ = 1
∙ 1 = 1. Is the process of simplifying
the
𝑥3−1 𝑥(𝑥2− 𝑥(𝑥+1) 𝑥 (𝑥+1)(𝑥−1) 𝑥 𝑥
1) (𝑥−1)
rational expression correct?

A. Yes, because the process followed the steps in simplifying rational expression.
B. Yes, because 𝑥
2
−1
is equivalent to 1 which is equal to1.
𝑥2−𝑥 1

C. No, because the factors in the denominator are incorrect.

D. No, because dividing out common factors were done incorrectly.

12. Suppose the city plaza has a perimeter of 4𝑠 and an area of 𝑠2. What is the ratio of the
area to the perimeter of the city plaza in simplest form?

A. 1
2 C. 𝑠
4
1
B.
D. 𝑠
2

𝑠
2

13. Suppose you are baking a cake with circular base whose volume is 𝜋𝑟2ℎ and surface
4

area of 2𝜋𝑟ℎ + 𝜋𝑟2. What is the ratio of the surface area to the volume of the cake in
simplest form?
𝑟ℎ
𝑟ℎ
A.
𝑟 2𝜋ℎ+
2ℎ+ C.
𝑟
𝑟 D. 𝜋𝑟ℎ
B. 2ℎ+
𝑟ℎ 2ℎ+𝑟

15
 𝑥+1
𝑥2−1
14. Is the rational expression in simplest form?

A. Yes, because the numerator and the denominator are in simplest form of a polynomial
expression.
B. Yes, because the numerator and the denominator have no common factor.
C. No, because the numerator and the denominator have different degrees.
D. No, because the denominator is not factored completely.

𝑥+1
15. Is the rational expression 1+𝑥 in simplest form?

A. Yes, because the numerator and the denominator are in simplest form of a polynomial
expression.
B. Yes, because the numerator and the denominator are both polynomial expression.
C. No, because negative one can still be factored from either the numerator or the
denominator.
D. No, because the numerator and the denominator can still be divide out.

Additional Activity

Express the given rational algebraic expression to its simplest form. Write your
answer on a separate sheet of paper.

3𝑥 6. 8𝑥3− 𝑦3
1. 6𝑥2 4𝑥2−𝑦2
2. 2𝑥+4 7. 𝑥2− 5𝑥+4
2𝑥−1 4+3𝑥−𝑥2
6

𝑎 3𝑏 3 8. 𝑏2− 𝑎2
3. 15
𝑎 4𝑏 4
20
𝑎3+𝑏3

𝑎2−𝑏2 9. 𝑥2+4𝑥+4
4. 7𝑎 +7𝑏
𝑎 −6𝑎
2 4−𝑥2

2𝑥2+5𝑥+2
+9
𝑎2−
2𝑥2+𝑥−6
5. 10.
9

16
16
References
Orlande A. Oronce, et al. (2013). Kto12 Worktext in Mathematics (Rex Book
Store,2013) pp 94-96

Teachers Guide in Mathematics 8 pp 76 – 80

Mathematics Learner’s Module 8; 2013 pp 66-71

Website Links

[Link]
[Link]
[Link]
[Link]

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