#1#2 #3#4 #5#6 #7#8 #9#10 #11#12 #13#14 #15#16 #17#18 #19 Rational Expressions Test (Study Guide #2) Simplify Name_________________1 1) 5) 8) 4) 3) 7)

#1 #2

#3 #4

#5 #6

#7 #8

#9 #10

#11 #12

#13 #14

#15 #16

#17 #18

#19

Rational Expressions Test (Study Guide #2)

Simplify

Name_________________1

2

2

x 7x 12x 9

1)

5)

8)

4)

3)

7)

2)

6)

3

2 2

x 1 2x8x x 1

x 3x 2

5x 10

2xy 2x3y 3xy

2

3x 4 3x 45x 10x

2 28x 1 2x 12x 2x

2 3x y

9)3x 1 x 8

3 4

x xx 1 x 3

11)10) 12)

Solve:

2 7x 5 x

x 1 5x 2 3x 12 3 6

14) 15)

1 1 3 x2x 4 3x

7 3 4x 2 2x x 2

x 13x 4 x

11x 7

x 3

Working together, Anne and Nichole can wallpaper an apartment in 12 hours. It would take Nichole 30 hours to do the job by herself. How long would it take Anne to do the job alone?

It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed?

17)16)2x 1 x 8

46 2x

18) Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute.

19)

Trader Joe’s has 200 lbs. of mixed nuts that is 10% peanuts. They want to create a trail mix that is 25% peanuts. How many pounds of peanuts must they add to the original mixed nuts?

20)

2

2

x 7x 12x 9

1)

5)

8)

4)

3)

7)

2)

6)

#1 #2

#3 #4

#5 #6

#7 #8

#9 #10

#11 #12

#13 #14

#15 #16

#17 #18

#19 #20

Rational Expressions Test (Study Guide #2)Simplify

Name_________________1

3

2 2

x 1 2x8x x 1

x 3x 2

5x 10

2xy 2x3y 3xy

2

3x 4 3x 45x 10x

2 28x 1 2x 12x 2x

2 3x y

9)

11)10) 12)

3x 1 x 83 4

x xx 1 x 3

Solve:

2 7x 5 x

x 1 5x 2 3x 12 3 6

14)13) 15)

1 1 3 x2x 4 3x

7 3 4x 2 2x x 2

x 13x 4 x

11x 7

x 3

x 4x 3

x4x 4

x 35 4x

9y

2x 5x

2y 3xxy 15x 20

12

2

4xx 2x 3

x 7

x 2 x 6

x 2 x 1,4

x 8, 4 x 1, 12

20 hours Mr. J ones: 60 mph

Working together, Anne and Nichole can wallpaper an apartment in 12 hours. It would take Nichole 30 hours to do the job by herself. How long would it take Anne to do the job alone?

It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed?

17)16)2x 1 x 8

46 2x

18) Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute.

19)

1 hour 12 minutes


20)

40 pounds

#1#1 Simplify

2

2

x 7x 12x 9

x 3 x 4

x 3 x 3

x 4x 3

Factor

Factor

Cancel CommonFactors!

x 43

x 3 x

x

3

#2#2 Simplify

3

2 2

x 1 2x8x x 1

x 1 2xxx2 2 2xx x 1 x 1

x4x 4

x 1 2xx2xx x

x2 12 x 1

Factor

Factor


#3#3

x 3x 2

5x 10

Multiply

x 2x 35x 10 1

x 35

Factor

x 2x 315 x 2


x 2

x 2

x 315

#4#4

2xy 2x3y 3xy


2 23yxy x

3xy

4x9y

Multiply

#5#5 Divide

2x


2

3x 4 3x 45x 10x

= Multiply by the reciprocal of the divisor

2

3x 4 10x3x 45x

3x 4 2 5x5xx 3x 4

23x 4 5x

5x 3xx 4

#6#6 Add

2 28x 1 2x 12x 2x

2 28x 1 2x 12x

C.L.T.

210x

2x

2 5xx

2x


2 5xx2x

5x

#7#7 Subtract

2 3x y

xy

2y 3x

Find a common denominator

2 3

yx yy x

x

#8#8

3x 1 x 83 4

Add

12

(3x 1) (x 8)4

43 433

12x 4 3x 24


15x 2012

C.L.T.

#9#9

x xx 1 x 3

Subtract

2

4xor

x 2x 3

(x 1)(x 3)

x x(x 3) (

xx 1)

1 x 3(x 3) (x 1)

2 2x 3x x x


Remember to distribute the negative when subtracting!

4x (x 1)(x 3)

#10#10 Solve

2 7x 5 x

2x 7x 35

5x 35

x 7

#11#11 Solve

x 1 5x 2 3x 12 3 6

x 1 5x 2 3x 1

2 3 66

x 1 5x 2 13 2 3x

3x 3 10x 4 3x 1

3x 3 7x 5

8 4x 2 x

#12#12 Solve1 1 3 x

2x 4 3x

1 1 3 x

12x2x 4 3x

6 3x 4 3 x

6 3x 12 4x

x 6

#13#13 7 3 4x 2 2x x 2

7 4 3x 2 x 2 2x

3 3x 2 2x

6x 3x 6

3x 6

x 2

Solve Move terms with common denominator to one side of the equation

This problem could have also been solved by multiplying both sides of the original equation by the common denominator of 2x and (x – 2)

#14#14

x 13x 4 x

Solve

2x 3x 4

2x 3x 4 0

x 4 x 1 0 x 4, 1

#15#15

11x 7

x 3

x 7 11

1 x 3

x 7 x 3 11 2x 4x 21 11

2x 4x 32 0

x 8 x 4 0 x 4,8

Solve

#16#16

2x 1 x 84

6 2x

Solve2x 1 x 8

46 2x

6x

x 2x + 1( ) + 4 6x( ) =3 x + 8( )

22x x 24x 3x 24 22x 22x 24 0

22 x 11x 12 0

2 x 12 x 1 0

x 12,1

#17#17 Working together, Anne and Nichole can wallpaper an apartment in 12 hours. It would take Nichole 30 hours to do the job by herself. How long would it take Anne to do the job alone?

1 1 130 x 12

x = hours it takes for Anne to do the job alone.

1 1 130 12

xx

60

Time Work Rate

Anne

Nichole

Tog

x

30

12

1

x

1

30

1

12

2x 60 5x 60 3x20 x

Anne 20 hrs.

#18#18 It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed?

Distance = rate x time

135

x = speed of Jones car

Smith135

x 15

180 x 180x

135

x −15=180

x

x - 15

Jones

#18#18 It took Mr. Jones as much time to drive 180 miles as it took Mr. Smith to drive 135 miles. Mr. Jones drove 15 mph faster than Mr. Smith. What was Mr. Jones’s speed?

135 180x 15 x

x = speed of Jones car

135x 180 x 15

135x 180x 2700

45x 2700 2700

x45

Mr. J ones 60 mph

Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems

#1#1 Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute.

Mr. P can write two tests in five hours. Mr. Lomas can write three tests in seven hours. If they work together, how long will it take them to write one test. Round your answer to the nearest minute.

Time Work Rate

Mr. P

Lomas

Tog

5

7

x

2

5

3

7

1

x

2

53

71

x

Homewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl emsHomewor k Pr obl ems

#19#19

1 hour 12 minutes

Multiply both sides by 35x

14x + 15x =35

=1

6

29 hours

29x =35

x =

35

29

2

53

71

x



20 x

0.25 200 x

#20#20

Original

New

PeanutsTotalMix

20 200

x = lbs. of peanuts to be added.

20 x 200 x

80 4x 200 x

3x 120

x 40

“have”

“want”

“stuff”

Add 40 lbs. of peanuts.

“stuff”

20 x 1

200 x 4


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#1#2 #3#4 #5#6 #7#8 #9#10 #11#12 #13#14 #15#16 #17#18 #19 Rational Expressions Test (Study Guide #2) Simplify Name_________________1 1) 5) 8) 4) 3) 7)