Free Printable Extra Practice: Simp., Mult., (some) Div. Rationals

1.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

2.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

3.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

4.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

5.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

6.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

7.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

8.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

9.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

10.

Simplify the rational expression

a)

A

b)

B

c)

C

d)

D

11.

Simplify

a)

$\frac{x+9}{x-9}$

b)

$\frac{1}{(x-9)}$

c)

$x-9$

d)

$\frac{1}{(x+9)}$

e)

$x+9$

12.

Simplify.

a)

$\frac{m+6}{m-3}$

b)

$\frac{7}{m-3}$

c)

$\frac{7}{m+6}$

d)

$\frac{1}{m+6}$

13.

Simplify.

a)

$\frac{1}{n-7}$

b)

$n-7$

c)

$\frac{(n-6)}{(n-7)}$

d)

$n-6$

14.

Simplify.

a)

$\frac{x+6}{x+4}$

b)

$\frac{1}{x-5}$

c)

$\frac{x+6}{x+5}$

d)

$\frac{x+6}{x-5}$

e)

$\frac{x+6}{\left(x+5\right)\left(x-4\right)}$

15.

Simplify the expression completely:

a)

A

b)

B

c)

C

d)

D

16.

Simplify and make sure final answer is in standard form.

a)

A

b)

B

c)

C

d)

D

17.

$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$

a)

$\frac{x-1}{x+7}$

b)

$\frac{x+1}{x+7}$

c)

$\frac{x-1}{x-7}$

d)

$\frac{x+1}{x-7}$

18.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

$\frac{x}{x+3}$

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

19.

$Simplify:\ \ \frac{x^2+7x+10}{x^2-4}$

a)

$\frac{x-5}{x+2}$

b)

$\frac{x-5}{x-2}$

c)

$\frac{x+5}{x+2}$

d)

$\frac{x+5}{x-2}$

20.

$Simplify:\ \ \frac{x^2-25}{x^2-6x+5}$

a)

$\frac{x+5}{x-1}$

b)

$\frac{x-5}{x-1}$

c)

$\frac{x+5}{x+1}$

d)

$\frac{x-5}{x+1}$

21.

$Simplify:\ \ \frac{x^2+7x+12}{x^2+4x}$

a)

$\frac{x+3}{x+4}$

b)

$\frac{x-3}{x}$

c)

$\frac{x+3}{x}$

d)

$\frac{x+3}{x^2}$

22.

$Simplify:\ \ \ \frac{x^2-4x-45}{x^2-81}$

a)

$\frac{x+5}{x-9}$

b)

$\frac{x+5}{x+9}$

c)

$\frac{x-5}{x-9}$

d)

$\frac{x-5}{x+9}$

23.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

24.

20x³/(5x+10)

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

25.

(-x-5)/(x²+12x+35)

a)

A. 1/(x+7)

b)

B. 1/(x-7)

c)

C. -1/(x+7)

d)

D. -1/(x+6)

26.

Simplify by cancelling

a)

1

b)

-1

c)

Can't be simplified

27.

Which of the following is equivalent?
(7-m)

a)

(m-7)

b)

-(m+7)

c)

-(7+m)

d)

-(m-7)

28.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

29.

Simplify.

a)

A.

b)

B.

c)

C.

d)

D.

30.

Simplify
(x²-49)/(x²+9x+14)

a)

(x-7)/(x+2)

b)

(x+7)/(x+2)

c)

(x-7)/(x-2)

d)

(x+7)/(x+2)

31.

Simplify
(x²+6x+8)/(x²-x-6)

a)

(x+2)/(x-3)

b)

(x+4)/(x+2)

c)

(x+4)/(x-3)

d)

(x+2)/(x+2)

32.

Simplify

(8x + 32)/( x+4)

a)

8/(x - 4)

b)

-x/(x - 4)

c)

-8

d)

8

33.

What is the excluded value:
7 / (x - 3)

a)

7

b)

There is not one.

c)

3

34.

$\ \frac{2x\left(x-2\right)}{\left(x-2\right)\left(x+5\right)}$

State the values of x which must be excluded to prevent division by zero.

a)

-2 and 5

b)

2 and -5

c)

0, 2, and -5

d)

0, -2, and 5

35.

$\frac{6}{6b-2}$

a)

$\frac{5b-2}{3b}$ ; {0}

b)

$\frac{3}{3b-1}$ ; {1/3}

c)

$\frac{1}{b+4}$ ; {2, -4}

d)

$\frac{3b-1}{3}$ ; no excluded values

36.

$\frac{x^2-3x-10}{x+2}$

a)

x-5 ;{-2}

b)

$\frac{4x^2}{x-1}$ ;{1}

c)

$\frac{x-1}{4x^2}$ ;{0}

d)

10; {-5}

37.

$\frac{25x^2+10x}{25x}$

a)

$\frac{5x+2}{5}$ ; {0}

b)

$\frac{5x}{3x+1}$ ;{0, -1/3}

c)

x - 1; {3}

d)

x - 5; {2}

38.

$\frac{x+1}{x^2+5x+4}$

a)

x-1; {-1}

b)

$\frac{5x+1}{3}$ ; {0}

c)

$\frac{3x-1}{3x}$ ;{0}

d)

$\frac{1}{x+4}$ ; {-4, -1}

39.

$\frac{x^2-5x+4}{x-1}$

a)

$\frac{2x}{2x+1}$ ; {0, -1/2}

b)

x-4; {1}

c)

$\frac{1}{5x}$ ; {0, 4}

d)

$\frac{2x+1}{2x}$ ; {0}

40.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

41.

$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$

a)

$\frac{x-1}{x+7}$

b)

$\frac{x+1}{x+7}$

c)

$\frac{x-1}{x-7}$

d)

$\frac{x+1}{x-7}$

42.

Simplify.

a)

$\frac{x+6}{x+4}$

b)

$\frac{1}{x-5}$

c)

$\frac{x+6}{x+5}$

d)

$\frac{x+6}{x-5}$

e)

$\frac{x+6}{\left(x+5\right)\left(x-4\right)}$

43.

Simplifying the rational expression. $\frac{2x^2-8x+8}{x^2-4}$

a)

$\frac{2\left(x-2\right)}{x+2}$

b)

$\frac{x-2}{x+2}$

c)

$\frac{2x-2}{x+2}$

d)

$\frac{2x+4}{x-2}$

44.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

45.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

46.

Find the product

a)

A

b)

B

c)

C

d)

D

47.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

48.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

49.

Simplify

a)

A

b)

B

c)

C

d)

D

50.

Simplify.

a)

A

b)

B

c)

C

d)

D

51.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

52.

a)

1 / 5p

b)

12 / 50p

c)

2 / 10p

d)

8 / 16p

53.

a)

7(r + 2)/ (r + 2)

b)

(r - 8) / (r + 2)

c)

(r + 2) / 7

d)

(r - 8) / 7

54.

Simplify.

a)

A

b)

B

c)

C

d)

D

55.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

56.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

57.

Simplify the expression.

a)

A

b)

B

c)

C

d)

D

58.

Simplify the expression.

a)

A

b)

B

c)

C

d)

D

59.

Simplify the expression.

a)

A

b)

B

c)

C

d)

D

60.

Simplify the expression.

a)

A

b)

B

c)

C

d)

D

61.

Simplify the expression.

a)

A

b)

B

c)

C

d)

D

62.

Simplify the expression.

a)

A

b)

B

c)

C

d)

D

63.

a)

7(r + 2)/ (r + 2)

b)

(r - 8) / (r + 2)

c)

(r + 2) / 7

d)

(r - 8) / 7

64.

a)

1 / (v + 7)

b)

5 / (v - 7)

c)

(v - 5)/(v + 7)

d)

5 / (v + 7)

65.

a)

(n + 4) / 10n

b)

(n + 4) 10

c)

1 / (n - 7)

d)

(n - 7) / 10n

66.

a)

5x / 3

b)

10x / (x - 8)

c)

10x

d)

6x(x - 8) / 6x

67.

a)

(x + 9)

b)

(x - 3) / (x + 2)

c)

(x + 9) / (x + 2)

d)

(x - 3)

68.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

69.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

70.

Simplify.

a)

A

b)

B

c)

C

d)

D

71.

Multiply.
$\frac{\left(x+3\right)}{\left(x-5\right)}\times\frac{x-5}{\left(x+3\right)\left(x-2\right)}$

a)

$\frac{1}{x-2}$

b)

$x-5$

c)

$4$

72.

$\frac{x+4}{x-2}\times\frac{\left(x-2\right)}{\left(x+1\right)}$

Multiply.

a)

$x\ +\ 1$

b)

$\frac{x+4}{x+1}$

c)

$\frac{x-2}{x}$

73.

Multiply.

\frac{\left(x\ +\ 7\right)}{8x\ +\ 40}\times\frac{x^2\ +9x\ +\ 20}{x\ -\ 8}

a)

$\frac{\left(x+7\right)\left(x+4\right)}{8\left(x-8\right)}$

b)

$x\ -\ 7$

c)

$\frac{8}{x\ +\ 7}$

74.

Multiply

\frac{6x\ -\ 12}{x^2\ +\ 9x\ +18}\times\frac{7x\ +\ 21}{5x\ -1\ 0}

a)

$\frac{42}{x+6}$

b)

$\left(x+3\right)\left(x-2\right)$

c)

$\frac{6\left(x-2\right)}{x\ +\ 6}$

75.

a)

(x + 9)

b)

(x - 3) / (x + 2)

c)

(x + 9) / (x + 2)

d)

(x - 3)

76.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

77.

a)

5x / 3

b)

10x / (x - 8)

c)

10x

d)

6x(x - 8) / 6x

78.

a)

A

b)

B

c)

C

d)

D

79.

a)

A

b)

B

c)

C

d)

D

80.

Simplify the expression

a)

1

b)

-1

c)

Can't be simplified

81.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

82.

Simplify.

a)

A.

b)

B.

c)

C.

d)

D.

83.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

84.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

85.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

86.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

87.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

88.

Simplify:
$\frac{x^2+10x+24}{x^2-x-20}$

a)

$\frac{x+6}{x+4}$

b)

$\left(x+6\right)\left(x+4\right)$

c)

$x+6$

d)

$\frac{x+6}{x-5}$

89.

$\frac{\left(x+9\right)\left(x+8\right)}{8}\cdot\frac{\left(x-1\right)}{\left(x+8\right)\left(x-1\right)}$

a)

$\frac{\left(x+9\right)}{8}$

b)

$\frac{\left(x-1\right)}{8}$

c)

$\frac{1}{8}$

d)

$\frac{\left(x+9\right)\left(x+8\right)}{8}$

90.

$\frac{x^2-x-6}{x-3}\cdot\frac{x+9}{x+2}$

a)

$x+9$

b)

$\frac{x-3}{x-2}$

c)

$\frac{x+9}{x+2}$

d)

$x-3$

91.

Multiply and Simplify:

\frac{x+3}{4}\cdot\frac{x+2}{x^2+4x+3}

a)

$\frac{4\left(x+3\right)}{x+2}$

b)

$\frac{x+2}{4\left(x+1\right)}$

c)

$\frac{x+2}{4\left(x+3\right)}$

d)

$\frac{4\left(x+1\right)}{\left(x+2\right)}$

92.

Multiply & Simplify:
$\frac{x^3-9x}{x^2+10x+21}\cdot\frac{x^2+7x}{x^2+5x-24}$

a)

$\frac{2x}{x+8}$

b)

$\frac{x^2}{x+8}$

c)

$\frac{x}{x+4}$

d)

$\frac{x^2\left(x-9\right)}{x+8}$

93.

Simplify:
$\frac{a-8}{7\left(a+2\right)}\cdot\frac{7\left(a+2\right)}{a+2}$

a)

$\frac{7\left(a+2\right)}{a+2}$

b)

$\frac{a-8}{a+2}$

c)

$\frac{a+2}{7}$

d)

$\frac{a-8}{7}$

94.

Multiply:
$\frac{2x+16}{x^2+3x-40}\cdot\frac{x^2-11x+30}{x^2-14x+48}$

a)

$\frac{3x^2\left(x+5\right)}{5}$

b)

$\frac{2}{x-8}$

c)

$x-2$

d)

$6x^2\left(x-4\right)$

95.

$\frac{8}{x-2}\cdot\frac{5x+50}{x+10}$

a)

$x+4$

b)

$x-4$

c)

$\frac{x+4}{5}$

d)

$\frac{40}{x-2}$

96.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

97.

Simplify

a)

A

b)

B

c)

C

d)

D

98.

a)

1 / 5p

b)

12 / 50p

c)

2 / 10p

d)

8 / 16p

99.

Suppose y varies directly as x.
If y = 22.5 when x = 15, find y when x = 20.

a)

1.5

b)

337.5

c)

30

d)

16.875

100.

Suppose y varies inversely with x.
If y = 150 when x = 2, find y when x = 25.

a)

300

b)

75

c)

1,875

d)

12

101.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

102.

The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.

a)

y = 4x

b)

y = 144x

c)

y = 4/x

d)

y = 144/x

103.

The Height of a wave in California varies directly with the seconds that pass by. At 4 seconds, the wave is 6 feet high. How many seconds will give you a wave that is 10 feet high?

a)

y = 2/3x

b)

6

c)

6.6

d)

7

104.

The number of kilograms of water in a person’s body varies directly as the person’s mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of water are in a person whose mass is 75 kg?

a)

50 kg water

b)

72 kg water

c)

94 kg water

d)

150 kg water

105.

The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?

a)

34.04

b)

90.00

c)

1,285.35

d)

44,444.44

106.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

107.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

108.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

109.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

110.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

111.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

112.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

113.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

114.

Divide the Rational Expression

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

115.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

116.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

117.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

118.

a)

A

b)

B

c)

C

d)

D

119.

a)

A

b)

B

c)

C

d)

D

120.

Simplify the expression

a)

1

b)

-1

c)

Can't be simplified

121.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

122.

Simplify.

a)

A.

b)

B.

c)

C.

d)

D.

123.

Simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

124.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

125.

For what value of a would the following system of equations have an infinite number of solutions?

2x − y = 8

and 6x − 3y = 4a

(number only)

(a)

Extra Practice: Simp., Mult., (some) Div. Rationals

Total questions: 125

Worksheet time: 11hrs 44mins

Similar Resources on Wayground