Main Ideas/Questions Notes/Examples

Rational Expressions

• A rational expression is a _____________________ of two polynomial expressions.

• Recall:

x + yy + x

=1 and

x − yy − x

= −1

Simplifying Expressions

Factor & Cancel

1.

64k 3 −14k2 −13k + 3

2.

12n2 − 48n288n2 −18n4

Multiplying & Dividing

Expressions

For Multiplication:

Factor, then simplify.

For Division: Multiply by the

reciprocal.

3.

x2 −10x − 24x3 + 2x2

⋅ 5x2 − 20xx2 −16x + 48

4.

5 p2 + 29p −65 p2 − 26 p + 5

⋅ 3 p2 −15 p36 − p2

5.

6s2 +11s + 41− 4s2

÷ 2s2 − s −12s2 − 3s +1

6.

k 4 −162k2 − k −6

÷ 4k 3 +16k12k2 +18k

Adding & subtracting Expressions

Get common denominators,

combine, then simplify

7.

34w

− 25w

8.

2x −1x + 4

− 3

Name: ___________________________________________________

Class: _________________________________

Date: _________________________________

Topic: ___________________________________________________

x y

© Gina Wilson (All Things Algebra®, LLC), 2017

9.

r + 5r2 − 25

+ 6r − 5

10.

5a +6a2 − 4

− 1a + 2

11.

q +1q − 4

− q −1q2 −7q +12

12.

3x +6

− 2x −1

Complex fractions

Combine the

numerator and denominator into a

single fraction, multiply by the reciprocal,

then simplify.

13.

110

− 940r2

13− 1

2r

14.

3 2

2 61

13

y y

y

+

+

15.

2

2

2

45 101 1

2

m nn m

n mn

+

+

© Gina Wilson (All Things Algebra®, LLC), 2017

Name: ___________________________________ Unit 1: Fundamental Skills

Date: ________________________ Per: ______ Homework 3: Rational Expressions

Directions: Simplify each expression.

1. 2

4 2

2 24 4x xx x

−−

2. 2

2

2036 9a aa a+ −−

3.

2k2 − 5k − 3k 3 − 27

Directions: Find each product or quotient. Give your answer in simplest form.

4. 2 2

3 2 2

2 24 36 12

x x x xx x x x+ − +⋅+ − −

5. 2

2 2

4 11 3 8 216 1 9w w ww w− − −⋅

− −

6. 2

4 2

1 11 1

c cc c

− +÷− +

7. 2 2

2 2

2 3 8 122 7 15 25m m m m

m m m+ +÷

− − −

Directions: Find each sum or difference. Give your answer in simplest form.

8. 2

1 36 4a a

− 9. 1

23

xx+−−

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© Gina Wilson (All Things Algebra®, LLC), 2017

10. 2

3 2 324 16

pp p

+++ −

11.

n2 + 7n −18n2 − 5n + 6

− 1n − 3

12. 2 17 4y y+

− − 13.

2 2

19 8 15

rr r r

−− + +

Directions: Simplify each complex fraction.

14.

2

14

8 2k

k k

−

− 15.

329

4

v

vv

+

−

16.

2

29 2

13 2

a bb aab b

−

+ 17.

2

2

1

14( )

xx

xx

+

+

18. Write an expression to represent the area of the rectangle below in simplest form.

© Gina Wilson (All Things Algebra®, LLC), 2017