Math 20-1 Chapter 6 Rational Expressions and Equations

6.2 Multiply and Divide Rational Expressions

Teacher Notes

6.2 Multiply and Divide Rational Expressions

To Multiply Rational Expressions• Factor the polynomials in each numerator and denominator.

• Given that if are two rational

expressions, then

• Divide out common factors in the numerator and denominator. Leave the remaining factors in factored form.

4 159 28

and , 0, 0 a c b db d

a c acb d bd

(2)(2)(3)(5)(3)(3)(2)(2)(7)

5(3)(7)

When you multiply rational expressions, follow procedures similar to those for multiplying rational numbers.

1 1

1

1

11

6.2.1

Multiply Rational Expressions

Multiply:4 3 2

2 3 5

80 1449 25

m x y

x y m

32 , 0, 0, 035

x m x y

my

4 3 2

53280 14

2549

m x ymx y

4 3 2

2 3 5

80 1449 25

m x yx y m

(5)(16)(2)(7) (7)(7)(5)(5)

x x x

xm m m m y y

y y my m m mx m

Factor the numerator and denominator.

Divide out the common factors.

(16)(2)(7)(5)

x

ym

6.2.2

Multiply Rational Expressions

Multiply: 2

27 7 20

4 7 42 49

x x xx x x

2

27 7 20

4 7 42 49

x x xx x x

7( 1) ( 5)( 4)4 7( 7)( 1)

x x x

x x x

Factor each numerator and denominator.

7( 1) ( 5)( 4)4 7( 7)( 1)

x x x

x x x Divide out common factors.

5 , 1, 4,77

x xx

List non-permissible values.

x = –4, x = 7, x = –1

Avoiding Mistakes:The domain of a rational expressionis always determined beforesimplifying the expression.

6.2.3

2 2

2

4 12 2 35 11 30 4

x x x xx x x

Your TurnMultiply and write the answer in simplest form

Multiply Rational Expressions

( 6)( 2)( 7)( 5) ( 6)( 5)( 4)

x x x xx x x

( 2)( 7) , 4, 5, 6( 4)

x x xx

NPVs: x = -4, x = -5, x = -6

6.2.4

Divide Rational Expressions

dc

ba

cd

ba

43

32

bcad

34

32

98

Multiply the dividend by the reciprocal of the divisor.

Example

6.2.5

Divide Rational Expressions

Multiply by the reciprocal

State NPVs

Divide out common factors.

Factor the numerator and denominator.

2 2

2 2

12 5 15 2 8 2

x x x xx x x x

Determine the quotient in simplest form

2 2

2 2

12 5 15 2 8 2

x x x xx x x x

2 2

2 2

12 2 • 2 8 5 15

x x x xx x x x

( 4)( 3)( 2)( 1)( 2)( 4)(5 )( 3)

x x x xx x x x

1, 3, 2,0,1,45

x x

x

6.2.6

Multiply and Divide Rational Expressions2 2

2 2

3 10 2 3 8 20 • 6 5 2 6 6 15

x x x x xx x x x x

2 2

2 2

3 10 2 3 8 20 • 6 5 2 6 6 15

x x x x xx x x x x

2 2

2 2

3 10 2 3 6 15 • • 6 5 2 6 8 20

x x x x xx x x x x

( 5)( 2)(2 3)( 1)(3)(2 5)=( 5)( 1)(2 3)( 2)(4)(2 5)

x x x x xx x x x x

3( 2) 5 3= , , ,–5, –2, –14 2

( 2) 2

x xx

Simplify

Multiply by the reciprocal

State NPVs

Divide out common factors.

Factor the numerator and denominator.

6.2.7

Your Turn

Multiply and Divide Rational Expressions

2 2 2 2

2 2

2 2 2 ( ) 4 4 3 6 3

m n m mn n m nm n m n m mn n

2 2 2 2

2 2

2 2 2 ( ) 4 4 3 6 3

m n m mn n m nm n m n m mn n

2 2

2 2 2 2

4 4 2 2 ( ) 2 3 6 3

m n m n m nm n m mn n m mn n

( )( )(4)( )(2)( )( )( )( )(3)( )( )

m n m n m n m n

m n m n m n m n m n

8= , 3( )

m nm n

( )( )(4)( )(2)( )( )( )( )(3)( )( )

m n m n m n m n

m n m n m n m n m n

6.2.8

Assignment

Suggested Questions:

Page 327:1a,b, 2a,d, 4b, 5, 6, 7a, 8a,d, 9, 10, 11, 14, 1517a, 20