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Name:_______________ Date:_______________ 5.0 Worksheet (2 pages) Simplify the following Rational Expressionsโ€ฆ.make sure answers are in FACTORED FORM. 1. (+) 2. (+)(โˆ’) + 3. โˆ’ โˆ’ 4. + + 5. (โˆ’) (โˆ’) 6. (โˆ’) 7. (โˆ’) + 8. โˆ’ (โˆ’) (โˆ’) 9. โˆ’ โˆ’+ 10. ++ โˆ’โˆ’ 11. โˆ’ โˆ’ 12. +โˆ’ โˆ’โˆ’

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Name:_______________ Date:_______________

5.0 Worksheet (2 pages) Simplify the following Rational Expressionsโ€ฆ.make sure answers are in FACTORED FORM.

1. ๐’™๐Ÿ(๐’™+๐Ÿ)

๐Ÿ”๐’™๐Ÿ“ 2.

(๐’™+๐Ÿ)(๐’™โˆ’๐Ÿ‘)

๐’™+๐Ÿ 3.

๐’‰โˆ’๐Ÿ

๐Ÿโˆ’๐’‰

4. ๐’™+๐Ÿ

๐’™+๐Ÿ 5.

๐Ÿ’๐’™(๐Ÿ๐’™โˆ’๐Ÿ)

๐Ÿ“๐’™(๐Ÿ‘๐’™โˆ’๐Ÿ) 6.

๐Ÿ–(๐’Œโˆ’๐Ÿ‘)

๐Ÿ”๐’Œ

7. ๐Ÿ(๐’™โˆ’๐Ÿ‘)

๐Ÿ๐’™+๐Ÿ• 8.

โˆ’๐Ÿ”๐’™๐Ÿ“๐’š๐Ÿ(๐’™โˆ’๐Ÿ)

๐Ÿ‘๐’™๐Ÿ“๐’š(๐’™โˆ’๐Ÿ) 9.

๐’Ž๐Ÿโˆ’๐Ÿ—

๐’Ž๐Ÿโˆ’๐Ÿ”๐’Ž+๐Ÿ—

10. ๐Ÿ”๐’™๐Ÿ+๐Ÿ“๐’™+๐Ÿ

๐Ÿ๐’™๐Ÿโˆ’๐Ÿ“๐’™โˆ’๐Ÿ‘ 11.

๐’‘๐Ÿโˆ’๐Ÿ‘๐Ÿ”

๐’‘โˆ’๐Ÿ” 12.

๐Ÿ‘๐’‚๐Ÿ+๐Ÿ“๐’‚โˆ’๐Ÿ

๐’‚๐Ÿโˆ’๐’‚โˆ’๐Ÿ”

Name:_______________ Date:_______________

Multiplying and Dividing Rational Expressionsโ€ฆmake sure answers are in FACTORED FORM.

13. ๐Ÿ๐Ÿ”๐’™๐Ÿ‘๐’š

๐Ÿ‘๐’™๐Ÿโˆ™๐Ÿ๐Ÿ•๐’š

๐Ÿ’๐’™๐Ÿ 14.

๐’Žโˆ’๐Ÿ•

๐’Žโˆ’๐Ÿโˆ™๐’Ž๐Ÿโˆ’๐Ÿ’

๐’Žโˆ’๐Ÿ• 15.

๐’‚๐Ÿโˆ’๐Ÿ๐Ÿ”

๐Ÿ๐’‚+๐Ÿ–โˆ™

๐’‚+๐Ÿ’

๐’‚๐Ÿ+๐Ÿ–๐’‚+๐Ÿ๐Ÿ”

16. ๐’Ž๐Ÿโˆ’๐Ÿ”๐’Ž+๐Ÿ—

๐Ÿ”โˆ™

๐Ÿ—

(๐’Žโˆ’๐Ÿ‘)๐Ÿ 17.

๐Ÿ—๐’‘๐’๐Ÿ‘

๐Ÿ’๐’Ž๐Ÿโˆ™๐Ÿ๐Ÿ๐’Ž๐Ÿ‘

๐Ÿ”๐’‘๐’ 18.

๐Ÿ”๐’Ž๐Ÿ๐’

๐Ÿ–โˆ™

๐Ÿ

๐Ÿ๐Ÿ–๐’Ž๐’

19. ๐’™๐Ÿโˆ’๐Ÿ‘๐Ÿ”

๐’™๐Ÿโˆ’๐Ÿ’๐Ÿ—รท

๐’™+๐Ÿ”

๐’™โˆ’๐Ÿ• 20.

๐Ÿ‘๐’š๐Ÿ‘โˆ’๐Ÿ๐Ÿ•๐’š

๐Ÿ๐’š๐Ÿ+๐Ÿ“๐’šโˆ’๐Ÿ‘รท

๐Ÿ—๐’š๐Ÿ

๐Ÿ’๐’š๐Ÿโˆ’๐Ÿ 21.

๐’‚๐Ÿโˆ’๐Ÿ“๐’‚+๐Ÿ”

๐Ÿ’รท

๐’‚โˆ’๐Ÿ‘

๐Ÿ๐Ÿ”

22. ๐’™๐Ÿ+๐’™

๐Ÿ”๐’™+๐Ÿ๐Ÿรท

๐’™๐Ÿโˆ’๐Ÿ

๐’™๐Ÿโˆ’๐Ÿ’ 23.

๐’™๐Ÿโˆ’๐Ÿ๐Ÿ”

๐Ÿ๐’™+๐Ÿ–รท

๐’™๐Ÿโˆ’๐Ÿ๐’™โˆ’๐Ÿ–

๐’™๐Ÿโˆ’๐’™โˆ’๐Ÿ” 24.

๐’™๐Ÿ โˆ’ ๐Ÿ๐Ÿ“

๐Ÿ๐’™ + ๐Ÿ๐ŸŽโˆ™๐’™๐Ÿ + ๐Ÿ“๐’™ + ๐Ÿ”

๐’™๐Ÿ โˆ’ ๐Ÿ‘๐Ÿ”รท

๐’™ + ๐Ÿ‘

๐Ÿ๐’™ + ๐Ÿ๐Ÿ

Name:_______________ Date:_______________

5.1 Worksheet (2 pages) Find the SUM or DIFFERENCE.

a. ๐‘ฅ2+3๐‘ฅ

๐‘ฅ+2+

2๐‘ฅ+6

๐‘ฅ+2 b.

7๐‘ฅ+3

๐‘ฅ2โˆ’1โˆ’

6

๐‘ฅโˆ’1

c. 7๐‘ฅ+3

๐‘ฅ2โˆ’1โˆ’

6๐‘ฅ+4

๐‘ฅ2โˆ’1

d. 6๐‘ฆ+13

๐‘ฆ2โˆ’4๐‘ฆโˆ’21โˆ’

๐‘ฆโˆ’2

๐‘ฆ2โˆ’4๐‘ฆโˆ’21

e. 4๐‘ฅ

๐‘ฅ2+9๐‘ฅ+18+

5

๐‘ฅ+6

f. 3๐‘Ž+6

๐‘Ž2โˆ’16โˆ’

7

6๐‘Ž+24

Name:_______________ Date:_______________

Simplify Each Complex Fraction.

g.

1

๐‘ฆ2โˆ’1

1+1

๐‘ฆ

h. 25

๐‘Žโˆ’๐‘Ž

5+๐‘Ž

i. 4+

12

2๐‘ฅโˆ’3

5+15

2๐‘ฅโˆ’3

j. ๐‘ฅ

3๐‘ฅโˆ’2๐‘ฅ

9๐‘ฅ2โˆ’4

Name:_______________ Date:_______________

5.2 Worksheet (2 pages) Solve each Rational Equation. Make sure to include all restrictions on Domain and

Check solutions for any extraneous solutions.

1. 1

6๐‘˜2=

1

3๐‘˜2โˆ’

1

๐‘˜ 2.

๐‘+6

4๐‘2+

3

2๐‘2=

๐‘+4

2๐‘2 3.

1

๐‘ฅ=

6

5๐‘ฅ+ 1

4. 1

๐‘ฃ+

3๐‘ฃ+12

๐‘ฃ2โˆ’5๐‘ฃ=

7๐‘ฃโˆ’56

๐‘ฃ2โˆ’5๐‘ฃ 5.

1

๐‘š2โˆ’๐‘š+

1

๐‘š=

5

๐‘š2โˆ’๐‘š 6.

1

๐‘›โˆ’8โˆ’ 1 =

7

๐‘›โˆ’8

7. 1

๐‘Ÿโˆ’2+

1

๐‘Ÿ2โˆ’7๐‘Ÿ+10=

6

๐‘Ÿโˆ’2 8. 1 =

๐‘ฃ+2

๐‘ฃโˆ’4+

7๐‘ฃโˆ’42

๐‘ฃโˆ’4 9.

๐‘Ÿโˆ’4

5๐‘Ÿ=

1

5๐‘Ÿ+ 1

Name:_______________ Date:_______________

10. 1 +๐‘ฅ2โˆ’5๐‘ฅโˆ’24

3๐‘ฅ=

๐‘ฅโˆ’6

3๐‘ฅ

11. 1 =1

๐‘ฅ2+2๐‘ฅ+

๐‘ฅโˆ’1

๐‘ฅ

12. ๐‘›+5

๐‘›+8= 1 +

6

๐‘›+1 13.

๐‘Ÿ+5

๐‘Ÿ2โˆ’2๐‘Ÿโˆ’ 1 =

1

๐‘Ÿ2โˆ’2๐‘Ÿ

14. ๐‘Žโˆ’2

๐‘Ž+3โˆ’ 1 =

3

๐‘Ž+2 15.

5

๐‘›3+2๐‘›2=

4

๐‘›+2+

1

๐‘›2

Name:_______________ Date:_______________

5.3 Worksheet (2 pages) Given the following Rational Functions. Identify the asymptotes, domain, and range of each function.

a) ๐’‡(๐’™) =๐Ÿ“

๐’™+๐Ÿ’ b) ๐’ˆ(๐’™) =

๐Ÿ–

๐’™โˆ’ ๐Ÿ‘

c) ๐’‡(๐’™) =๐Ÿ

๐’™+๐Ÿ”โˆ’ ๐Ÿ d) ๐’‰(๐’™) =

โˆ’๐Ÿ‘

๐’™โˆ’๐Ÿ+ ๐Ÿ“

e) ๐’ˆ(๐’™) =๐Ÿ“

๐’™ f) ๐’“(๐’™) =

โˆ’๐Ÿ

๐’™โˆ’๐Ÿ+ ๐Ÿ’

g) ๐’ƒ(๐’™) =๐Ÿ‘

๐Ÿ๐’™โˆ’๐Ÿ’ h) ๐’Ž(๐’™) =

๐Ÿ

๐Ÿ’๐’™+๐Ÿโˆ’ ๐Ÿ•

Name:_______________ Date:_______________

Graph each function. State the Domain and Range.

i) ๐’‡(๐’™) =๐Ÿ‘

๐’™โˆ’๐Ÿ•โˆ’ ๐Ÿ–

j) ๐’‰(๐’™) =โˆ’๐Ÿ”

๐’™+๐Ÿ’โˆ’ ๐Ÿ

k) ๐’ˆ(๐’™) =๐Ÿ‘

๐’™โˆ’ ๐Ÿ“

l) ๐’Ž(๐’™) =โˆ’๐Ÿ

๐Ÿ

๐Ÿ’๐’™โˆ’๐Ÿ

+ ๐Ÿ

Name:_______________ Date:_______________

5.4 Worksheet (1 page) For the following Functions, find (if they apply to the function):

a) the vertical asymptote(s)

b) the horiztonal/slant asymptotes

c) the holes

1. ๐‘“(๐‘ฅ) =2๐‘ฅ

๐‘ฅ2โˆ’1 2. ๐‘š(๐‘ฅ) =

๐‘ฅ2โˆ’5๐‘ฅ+6

๐‘ฅ2โˆ’4๐‘ฅ+3

3. ๐‘”(๐‘ฅ) =8

๐‘ฅ2โˆ’๐‘ฅโˆ’6 4. ๐‘“(๐‘ฅ) =

๐‘ฅ2+11๐‘ฅ+18

2๐‘ฅ+1

5. โ„Ž(๐‘ฅ) =๐‘ฅ2โˆ’9

2๐‘ฅ2+1 6. ๐‘(๐‘ฅ) =

๐‘ฅโˆ’4

๐‘ฅ2โˆ’3๐‘ฅ

Name:_______________ Date:_______________

5.5 Worksheet (2 pages) For the following Functions, find (if they apply to the function):

a) the ๐’™-intercepts, and ๐’š-intercepts

b) the vertical asymptote(s)

c) the horiztonal/slant asymptotes

d) the holes

e) any additional points needed

f) then, graph each function

7. ๐‘“(๐‘ฅ) =2๐‘ฅ

๐‘ฅ2โˆ’1

8. ๐‘š(๐‘ฅ) =๐‘ฅ2โˆ’5๐‘ฅ+6

๐‘ฅ2โˆ’4๐‘ฅ+3

Name:_______________ Date:_______________

9. ๐‘”(๐‘ฅ) =8

๐‘ฅ2โˆ’๐‘ฅโˆ’6

10. ๐‘“(๐‘ฅ) =๐‘ฅ2+11๐‘ฅ+18

2๐‘ฅ+1

11. โ„Ž(๐‘ฅ) =๐‘ฅ2โˆ’9

2๐‘ฅ2+1

12. ๐‘(๐‘ฅ) =๐‘ฅโˆ’4

๐‘ฅ2โˆ’3๐‘ฅ

Name:_______________ Date:_______________

5.6 Worksheet (2 pages) Solve Each Rational Inequality. Write answers in interval notation.

1. 3 โˆ’4

๐‘ฅ>

5

4๐‘ฅ 2.

5

3๐‘Žโˆ’

3

4๐‘Ž>

5

6

3. ๐‘ฅโˆ’2

๐‘ฅ+2+

1

๐‘ฅโˆ’2>

๐‘ฅโˆ’4

๐‘ฅโˆ’2 4.

3

4โˆ’

1

๐‘ฅโˆ’3>

๐‘ฅ

๐‘ฅ+4

Name:_______________ Date:_______________

5. ๐‘ฅ

5+

2

3<

3

๐‘ฅโˆ’4 6.

๐‘ฅ

๐‘ฅ+2+

1

๐‘ฅโˆ’1<

3

2

7. โˆ’7

๐‘ฅ+5โ‰ค โˆ’

8

๐‘ฅ+6 8.

(๐‘ฅ+7)(๐‘ฅโˆ’3)

(๐‘ฅโˆ’5)2> 0

9. Upper Levelโ€ฆ..Extra Credit

Solve 1+

9

๐‘ฅ+20

๐‘ฅ2

1โˆ’25

๐‘ฅ2

=๐‘ฅ+4

๐‘ฅโˆ’5