length, height, and width to find the dimensions of the shed when x = 4 feet. ... Alexa can bike home from school an hour and a half faster than she c...

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Rational Expressions and Equations

MODULE

9

Study Guide

1. Is each of the following an excluded value of the rational expression x 2 2x ? x 2 2x 8

5.

x 5 2 x 11x 30 x 9 x 20 2

________________________________________

A 4

Yes

No

B 2

Yes

No

C 0

Yes

No

D 2

Yes

No

E 4

Yes

No

2. Write the expression below as an equivalent expression with a denominator of ( x 2 4)( x 1) .

6.

________________________________________

7. Is each of the following an excluded value of the quotient ( x 3)( x 2 36) 2x 12 ? 3x x2 9

6x 2x 4 _______________________________________

3. Determine if each expression is x 2 3 x 10 equivalent to 2 . Choose ( x 25)( x 2) True or False. A

2x (5 x )(2 x )

True

False

B

x 2 ( x 5)( x 2)

True

False

C

x 2 ( x 5)( x 2)

True

False

D

2x ( x 5)( x 2)

True

False

For 4–6, add or subtract the given expressions. Give each result in simplest form and state the combined excluded values. 9 4. x 3 x 3 _______________________________________

4 6 3x 2 x 1 x 1 x 1

A 6

Yes

No

B 3

Yes

No

C 0

Yes

No

D 3

Yes

No

E 6

Yes

No

For 8–11, multiply or divide the given expressions. Give each result in simplest form and state any excluded values. 8.

2x 2 x 2 6x

x4 3x 3

________________________________________

9.

x2 x 6 x 2 x 20

x 2 6x 8 x2

________________________________________

10.

x 2 4 x 21 x 2 8 x 15 2 x 2 49 x 2x 35 ________________________________________

11.

x 2 4 x 4 2x 2 x 3 x 2 7 x 12 x 2 3 x ________________________________________

Name _______________________________________ Date __________________ Class __________________ MODULE

9

Rational Expressions and Equations Study Guide

12. The volume of a rectangular garden shed is given by the expression x 4 x 3 6x 2 . The length of the shed is given by the expression 3x 6 and the height of the shed is given by the expression x2 9. Find a rational expression for the width of the shed. Then use the expressions for length, height, and width to find the dimensions of the shed when x 4 feet.

17.Does each set of rational expressions have the LCD 4( x 1)( x 2)( x 2)? A

x2 3x , 2 4 x 4 2x 2 8

Yes

No

B

x x 3 , 2x 2 4 x 2 16

Yes

No

C

x 5 x , 2 4x 8 x 3x 2

Yes

No

D

x6 x 3 , 2 2x 4 4 x 4 x 8

Yes

No

_______________________________________ _______________________________________

13. Solve the rational equation. x 4 x 5 _______________________________________

For 14–16, solve each rational equation algebraically. 14.

2x x 2 x 9 x 1 _______________________________________

15.

24 3 4 x 16 x 4 x 4 2

_______________________________________

16.

5x 2 x 3 x 10 2

_______________________________________

18. Alexa can bike home from school an hour and a half faster than she can walk home. Her biking speed is 9 miles per hour faster than her walking speed. Her school is 6 miles from her home. Write an equation that can be used to find her walking speed, w. Do not solve. ________________________________________

19. Marcus can empty his swimming pool in 2 hours if he uses both of his hoses, which have different diameters. Using only the smaller hose, it takes 3 hours longer to drain the pool than when using only the larger hose. Write an equation that can be used to find the time, t, that it takes Marcus to drain the pool using only the larger hose. How long does it take Marcus to drain the pool using only the smaller hose? ________________________________________

Name _______________________________________ Date __________________ Class __________________

MODULE 9 Rational Expressions and Equations

Study Guide 1. A No B Yes C No D No E Yes 2.

3 x( x 2)( x 1) ( x 2 4)( x 1)

3. A True B False C True D False 4.

x2 ; x 3 x 3

5.

x 6 ; x 6, 5, 4 ( x 6)( x 4)

6.

3x 2 ; x 1, 1 x 1

7. A No B Yes C Yes D Yes E Yes 8.

2( x 4) ; x 6, 0, 1 3 x( x 6)

9.

( x 3)( x 2) ; x 5, 2, 4 x 5

10.

x 3 ; x 7, 5, 3, 7 x 3

11.

x 2 ; x 4, 3, 0, 2 x( x 4)

12. w

x2 1 ; l 6 ft, h 7 ft, w 5 ft 3( x 3) 3

14. x 3 and x 6 15. no solution 16. x

5 2

17. A No B Yes C No D Yes 18.

6 6 3 w w 9 2

19.

2 2 1; 6 hr t t 3

13.

x =4