Adding and Subtracting Rational Expressions

Name California Standards LESSON

Date 13.0,

Class

15.0

Review for Mastery

10-5 Adding and Subtracting Rational Expressions The rules for adding and subtracting rational expressions are the same as the rules for adding and subtracting fractions. 6 2 ! __ 4"2 ! 4 " __ __ _____ 7

7

7

3 4 # __ 1"4 # 1 " __ __ _____

7

5

5

5

5

10 . " 10 " _______ _______ Add 5x 2 2 x ! 16 x ! 16 Simplify your answer. 5x ! 10 ! _______ 10 _______ x 2 # 16 x 2 # 16

x!3 . 2x ! _______ Subtract _______ 2 2x " 6 2x 2 " 6 Simplify your answer. x#3 2x _______ # _______ 2x 2 ! 6 2x 2 ! 6

! 5x ! 10 " ! 10 _____________

Add numerators.

2x # !x # 3 " ___________ 2x 2 ! 6

Subtract numerators.

5x ! 20 _______ x 2 # 16

Add like terms.

2x #x!3 _________ 2x 2 ! 6

Distribute !1.

5 !x ! 4 " _____________ !x ! 4 " !x # 4 "

Factor.

x!3 _______

Combine like terms.

1 5 !x ! 4 " ______________ 1 !x ! 4 " !x # 4 "

Simplify.

x!3 ________ 2 !x ! 3 "

Factor.

2

x # 16

2x 2 ! 6

1

x!3 _________ ! 2 x ! 3 "1

5 _____

x#4

Simplify.

1 __ 2

Add or subtract. Simplify your answer. 8 x ! 2 ! ________ 1. ________ x 2 # 100 x 2 # 100

2

# 18 ! _____ 3x 2. x_______ x!6 x!6

1 ______

1 ____ 10x

Copyright © by Holt, Rinehart and Winston. All rights reserved.

1 __

x!3

x ! 10

x 2 4. __________ # __________ 2 2 10x # 20x 10x # 20x

6 x 3. _______ ! _______ 5x ! 30 5x ! 30

2

5

2

25 # 4x x x _______ # 12 5. ___________ # ___________ 6. _____ 2 2 x!6 x!6 x ! 10x ! 25 x ! 10x ! 25

x !5 _____ x"5

137

x!2

Holt Algebra 1

Name California Standards

Date 13.0,

Class

15.0

Review for Mastery

LESSON

10-5 Adding and Subtracting Rational Expressions continued Like fractions, you may need to multiply by a form of 1 to obtain common denominators.

! "

! "

5 ! ___ 5 ! ___ 8 " ___ 13 1 ! ___ 4 __ 2 " ___ 4 " __ 1 __ __ 6

15

6 5

15 2

10x

2 The LCD is 10x .

5x

!2 "

3 __ x ! ___ 2 __ 2 ____ 2 x 10x !

"

5x

x#4

3x !4 ______ 10x 2

Add numerators.

5 and ____ 13 . 7. Identify the LCD of ___ 2 20x 8x 3 and _____ x . 8. Identify the LCD of ___ 5x x!7 Add or subtract. Simplify your answer. 5 2x ! ____ 9. ___ 3 12x 8x

Add numerators.

5x ! x ! 7 "

5x ! 11 # _____ 4 10. __________ 2 x!3 x ! 5x ! 6

! " ! "

! x ! 3 "! x ! 2 "

5x !3 ______ 2 12x 4x ! _____ 2 11. ___ 6x x!4

2x ! 14 _______ 3x ! 12 Copyright © by Holt, Rinehart and Winston. All rights reserved.

! " x!2

5x ! 11 4 _____ ______________ # _____

12x 2x

3

8 _____

40x 2

5 ____ 2x ____ ! ____ ___ 3 2 8x

Multiply.

x#4

x#4

2x 2

3

the second ! " Multiply term by a form of 1.

4 # x #1

3 # _____ #5 _____ x#4

Multiply.

30

3 # _____ 5 #1 _____ ___

Multiply each term by a form of 1.

3x ! ____ 4 ____ 2 10x 10x 2

30

5 . 3 " _____ Subtract _____ x"4 4"x Simplify your answer. 3 # _____ 5 _____ The LCD is x # 4. x#4 4#x

3 ! ____ 2 . Add ____ 10x 5x 2 Simplify your answer. 3 ! ___ 2 ____ 2

30

x!3 x!2

1 _____

x!2

3x # 6 # _____ 2 12. _______ 2 x ! 6 x # 36

1 _____

x"6

138

2x 1 13. __________ ! _____ 2 x ! 1 x ! 4x ! 3

x _____

x!3 Holt Algebra 1