Manipulations of Rational Expression

Objectives

a) Differentiate rational Numbers from Rational Expression

b) Simplify rational expression

c) Multiply and divide rational expression

d) Add and subtract rational expression

e) Simplify complex fraction

f) Participate actively in class discussion

GROUP ACTIVITY

Directions:

Analyze the following numbers whether a Rational Expression or Rational Numbers.

You only have 5 minutes for this activity.

• 2/-3• 2x2+7x/x + 1• -1/5• 6x/6• 9x2-1/4x2 + 5• 25/3x• 10x2 +4x + 9/ x2 + 4• 8/5• 1• 0• X2 + 4x + 4/ x2 – 1• 2x + 10/ x + 5• 2x + 8/ 3x + 12• 1/ x• 2/3

Correct Answer

RATIONAL NUMBERS

1.2/-3

2.-1/5

3.8/5

4.2/3

RATIONAL EXPRESSION

1.2x2+7x/x + 1

2.9x2-1/4x2 + 5

3.10x2 +4x + 9/ x2 + 4

4.X2 + 4x + 4/ x2 – 1

5.X2 + 4x + 4/ x2 – 1

6.2x + 10/ x + 5

7.2x + 8/ 3x + 12

DIFFERENTIATE

RATIONAL

NUMBERS 1.2/-3

2.-1/5

a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero

RATIONAL

EXPRESSIONS1.2x2+7x/x + 1

2.9x2-1/4x2 + 5

A rational expression is nothing more than a fraction in which the numerator and/or the denominator are polynomials.

FACTORIZATION RATIONAL EXPRESSION

EQUALS TO:

SIMPLIFYING RATIONAL EXPRESSION

SIMPLIFY:1. X – 1

5x - 5

Solutions:

= (x – 1)

5( x – 1)

= (x – 1)

5( x – 1)

Final answer:

1

5

STEPS:

1. Look for the GCF or the common factor of the numerator and denominator.

2. Cancel the common factor.

SIMPLIFY THE EXPRESSION2. xy + 3y

4x + 12

Solution:

= y ( x + 3)

4 ( x + 3)

= y ( x + 3)

4 ( x + 3)

Final Answer:

y

4

Steps:

1. Look for the GCF or the common factor of the numerator and denominator.

2. Cancel the common factor.

YOUR TURN!

GROUP 1:

4b + 8a GROUP 4:bc + 2ac 2x + 8

3x + 12GROUP 2:2xy + 4y2

x2 + 2xy

GROUP 3:2x + 10 x + 5

GENERALIZATION

What is Rational Expression?

What is Rational Numbers?

What are the steps in simplifying rational expression?

INDIVIDUAL SEATWORK

• Get ½ crosswise.

Direction: Simplify the following expression

1.5x2 + 20 2x + 8

2.21xy + 6y2

42x + 12y

3.2x2 + 2x

3x2 + 3x

4. x – 1

x2 – 1

5. p2 – p -6

p - 3

CORRECT ANSWER

1.5 /2

2.3y/6 or y/2

3.2x/3x

4.1/x + 1

5. p + 2/ 1

Assignment:

Study about Multiplication and Division of Rational Expression. Pop – up quiz tomorrow.

THANK YOU FOR YOUR COOPERATION!! ^_^