Rational Expression Test Problems)

ID: 1

Algebra 1

Name___________________________________

Assignment

Date________________ Period____

Simplify each and state the excluded values. 1)

9x + x x + x+ 9

2)

a− a−

3)

m + m+8 m − m−

4)

v + 9v + v − v−

5)

m − m + m+

Simplify each expression. 6)

8)

k k+

x+

k k

−

−

x+

10)

8v + v v−

12)

p+ p−

14)

8 8x − x x+

16)

x−

p−

9)

m+

11)

p p

−

÷

7)

x− x−

x−8

+

−

−

13)

8 x+

+

15)

8 x+

−

17)

b+ b+

÷

p−

m+

8 x−

x−

x−

b +b− 8b −

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18)

20)

22)

b + b− b−

÷

÷

x − x+ k− k−

n + 9n

19)

x−

23)

x ⋅ x x−

25)

⋅

n

p− ⋅ p +8 p−

21)

k + k− ⋅ k+

x − x +

24)

b+ b

x −

÷

x+

k −

k

÷

x−8

k−8 k − k

Solve each equation. Remember to check for extraneous solutions. 26)

28)

30)

32)

34)

=

x

+

x

x

=

=

n

m+

x− x

+

n

−

x −

27)

29)

x

+

31)

n

m + m

x−

=

=

33)

m + m

x −

x−8

−

x+

35)

x

x

x+ x

+

+

x+ x

=

=

x

x

x+ = x + x x+

=

v−

m

−

v − v

−

−

x + x

v+ v − v

m− = m + 8m m+8

Simplify each and state the excluded values. 36)

n+ n+

37)

38)

v+8 v+

39)

n +

n+ n+

k − 9k + 9 k+

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40)

x− x − x+

41) How much soil with 32% sand do you need to add to 6 m³ of soil with 56% sand in order to make a soil with 48% sand?

42) How many kg of a metal containing 90% silver must be combined with 11 kg of a metal containing 10% silver to form an alloy containing 46% silver?

43) Sarawong wants to make a 32% alcohol solution. He has already poured 12 L of a 14% alcohol solution into a beaker. How many L of a 68% alcohol solution must he add to this to create the desired mixture?

44) How much of Brand A fruit punch (55% fruit juice) must be mixed with 4 L of grape juice to create a mixture containing 85% fruit juice?

45) How many L of a 66% acid solution must be mixed with 8 L of a 56% acid solution to make a 62% solution?

Solve each question. Round your answer to the nearest hundredth. 46) Kim can dig a 10 ft by 10 ft hole in 8.2 hours. Beth can dig the same hole in 9.7 hours. How long would it take them if they worked together?

47) It takes Norachai eight hours to pick forty bushels of apples. Cody can pick the same amount in 14 hours. Find how long it would take them if they worked together.

48) Molly can harvest a field in 9.7 hours. Amanda can harvest the same field in 8.8 hours. If they worked together how long would it take them?

49) It takes Norachai nine hours to oil the lanes in a bowling alley. Jacob can oil the same lanes in 8.5 hours. How long would it take them if they worked together?

50) Jenny can sweep a porch in 15 minutes. Maria can sweep the same porch in 10 minutes. If they worked together how long would it take them?

51) Working together, Natalie and Matt can sweep a porch in 5.32 minutes. Had he done it alone it would have taken Matt 13 minutes. Find how long it would take Natalie to do it alone.

52) Julio can pick forty bushels of apples in 11 hours. Jacob can pick the same amount in 14 hours. Find how long it would take them if they worked together.

53) It takes Stephanie nine hours to mop a warehouse. Totsakan can mop the same warehouse in 12 hours. How long would it take them if they worked together?

54) Working alone, it takes Krystal 11 hours to harvest a field. Kayla can harvest the same field in 10 hours. How long would it take them if they worked together?

55) Working alone, Trevon can pick forty bushels of apples in 15 hours. One day his friend Elisa helped him and it only took 7.24 hours. Find how long it would take Elisa to do it alone.

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Answers to Assignment (ID: 1) 9x ; {− } x+ m−8 5) ; {−8} m+8 m+ 9) (m + )(m + ) x− 13) (x + )(x − ) 8 17) b+ 1)

21)

p+8

k− 29) {− } 33) { } n+

; {− }

; { } x− 44) 2 L 48) 4.61 hours 52) 6.16 hours 40)

6) 10) 14) 18)

a− ; { } a− k− (k + ) v+ v− + x − 8x x(x + ) b

(k − )(k − ) k− 26) { 8} 22)

25)

37)

2)

3)

m+ m−

; {− , }

p− 9 ( p − )(p − ) − x+ 11) (x − )(x − 8) x− 15) (x + )(x − ) 19) n + 7)

23)

x−

4)

v+ v−

; {− , }

x ( x + )(x + ) −p + 8 12) (p − ) 16) x − 8) −

20)

x−

24)

x+

27) {− }

28) { }

30) {− } 34) { }

31) { } 35) {8}

(v + ) ; {− } v+ 41) 3 m³

32) { } (n + ) 9 36) ; {− } n +9

38)

39)

45) 12 L 49) 4.37 hours 53) 5.14 hours

46) 4.44 hours 50) 6 minutes 54) 5.24 hours

(k − 9)(k − ) ; {− } (k + ) 42) 9 kg 43) 6 L

47) 5.09 hours 51) 9.01 minutes 55) 13.99 hours

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