Warm- upWarm- up

Factor completely:

4

4 3 2

16 64p

c c c c

Simplify, Multiply and Simplify, Multiply and Divide Rational Divide Rational

ExpressionsExpressionsObjectives:

•To simplify rational expressions, and•Simplify complex fractions

Rational algebraic expressionsRational algebraic expressions

A rational algebraic expression can be expressed as the quotient of two polynomials.

◦Note: The denominator can NEVER be 0.

Rational ExpressionRational Expression

Property: Let a, b, and c be expressions with and

Then the following property applies:

 

0b 0.c

ac

bc

Simplified Form of a Rational Simplified Form of a Rational ExpressionExpression

A rational expression is in SIMPLIFIED FORM if its numerator and DENOMINATOR have no common factors other than

 1

procedureprocedure

1. Factor the numerator and denominator.

2. Divide out any factors that are common to both.

3. State the excluded values by setting the denominator =0 and solving.

Example: 2

2

7x x

x

BIG NO NOBIG NO NO

1. Factor the numerator and denominator.

2. Divide out any factors that are common to both.

3. State the excluded values by setting the denominator =0 and solving.

Example: 2

2

7x x

x

Simply rational expressionsSimply rational expressions

Example 1

2

2 ( 1)

( 1)( 4)

x x

x x

Simply rational expressionsSimply rational expressions

Example #2

2 2

2

2 ( 4)( 3).

8 ( 2)( 4)

a a b

ab a a

Simplify rational expressionsSimplify rational expressions

Example 3: Simplify:

2 4

3

3

2 6

a a

a a

Simplify rational expressionsSimplify rational expressions

Example 4: Simplify:

2

2

2 10

3 16 5

x x

x x

Multiply fractions/rational Multiply fractions/rational expressionsexpressions

Recall to multiply two fractions or rational expressions, you first multiply the numerators and then multiply the denominators.

3 2 3 10

4 15 5 9

MULTIPLYING PROCEDUREMULTIPLYING PROCEDURE

1. MULTIPLY THE NUMERATORS.

2. MULTIPLY THE DENOMINATORS.

3. WRITE THE NEW FRACTION IN SIMPLIFIED FORM.

Multiply rational expressionsMultiply rational expressions

Example 5: Multiply:

Recall to multiply two fractions or rational expressions, you first multiply the numerators and then multiply the denominators.

2 2

2 3

2 3

5 8

a bc

b c a

Multiply rational expressionsMultiply rational expressions

Example 6: Multiply:

Example 7: Multiply:

3

2

7 63

9 35

a b

b a

2

3 2 3

14 24

9 35

c d mn

m n cd

Multiply rational expressionsMultiply rational expressions

Example 8: Multiply:

2 2

2

3 3 20

4 5 3

a a a a

a a a

Dividing ProcedureDividing Procedure

1. Multiply by the reciprocal2. Simplify.

Divide rational expressionsDivide rational expressions

Example 9

2 2

2 4

8 2

15 5

x y xy

a b ab

Divide rational expressionsDivide rational expressions

Example 10: Divide: 2 3

3 2

14 35

9 24

c d cd

m n mn

Divide rational expressionsDivide rational expressions

Example 11: Divide: 2

2

2 8 2

4 3 3 3

x x x

x x x

Divide rational expressionsDivide rational expressions

Example 12: Divide:2 2

2 ( 2)

5 25

y y y

y y y

In groups of 4In groups of 4

Person 1: Write two rational expressions using the same variables

Person 2: Simplify the expressionPerson 3: Multiply the two expressionsPerson 4: Divide the two expressions

DISCUSSROTATE AND REPREAT

TOTDTOTD

Explain under what conditions a rational polynomial expression is not defined.

homeworkhomework

Kuta worksheet