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6.1-6.2 Practice

Total questions: 164

Worksheet time: 13hrs 0mins

Name
Class
Date
1.
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
2.
Simplify. 
a)
(m+6)/(m-3)
b)
7/(m-3)
c)
7(m+6)
d)
(m-3)
3.
Simplify. 
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
4.
SIMPLIFY
a)
A
b)
B
c)
C
d)
D
5.
Simplify 
a)
A.(x+7)/(x-4)
b)
B.-3/4
c)
C.(x+3)/(x+4)
d)
D.(x+3)/(x-4)
6.
a)
A
b)
B
c)
C
d)
D
7.
Simplify.
a)
1/(n-7)
b)
n-7
c)
(n-6)/(n-7)
d)
n-6
8.
a)
A
b)
B
c)
C
d)
D
9.
a)
A
b)
B
c)
C
d)
D
10.
a)
A
b)
B
c)
C
d)
D
11.
a)
A
b)
B
c)
C
d)
D
12.
a)
A
b)
B
c)
C
d)
D
13.
a)
A
b)
B
c)
C
d)
D
14.
a)
A
b)
B
c)
C
d)
D
15.
a)
A
b)
B
c)
C
d)
D
16.
a)
A
b)
B
c)
 C
d)
 D
17.
Simplify.
a)
A.
b)
B.
c)
C.
d)
D.
18.
Find the Excluded Value of 32n2/24n
a)
n = 0
b)
n = 24
c)
n = -24
d)
n can be any real number
19.
Factor Completely: 
x4-9x2
Hint: Factor GCF first. 
a)
x2(x+3)(x-3)
b)
(x2+3x)(x2-3x)
c)
(x2+9)(x-3)(x+3)
d)
x2(x2-9)
20.
Simplify
a)
A
b)
B
c)
C
d)
D
21.
Simplify
a)
A.4x³/(x+2)
b)
B.4x³/(x+10)
c)
C.2x³/(5x+1)
d)
D. 2x³/(x+5)
22.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
23.
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), 
24.
Multiply and Simplify
a)
(n-10)/8n+56
b)
(n-10)(n+7)/8n+56
c)
(n-10)/8
d)
(n+10)/8
25.
Simplify. 
a)
(m+6)/(m-3)
b)
7/(m-3)
c)
7(m+6)
d)
(m-3)
26.

Simplify.

a)

A

b)

B

c)

C

d)

D

27.
Divide and Simplify
a)
A
b)
B
c)
C
d)
D
28.
Simplify.
a)
1/(n-7)
b)
n-7
c)
(n-6)/(n-7)
d)
n-6
29.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
30.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
31.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
32.
Simplify. 
a)
A
b)
B
c)
C
d)
D
33.

Simplify 7n3n−18+n+33\frac{7n}{3n-18}+\frac{n+3}{3}  

a)

8n+33n−15\frac{8n+3}{3n-15}  

b)

n2+4n−183(n−6)\frac{n^2+4n-18}{3\left(n-6\right)}  

c)

7(n+3)3(3n−18)\frac{7\left(n+3\right)}{3\left(3n-18\right)}  

d)

7n+n+33n−18+3\frac{7n+n+3}{3n-18+3}  

34.

Simplify 8nn−3+3n5n−6\frac{8n}{n-3}+\frac{3n}{5n-6}  

a)

43n2−9(5n−6)(n−3)\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}  

b)

11n6n−9\frac{11n}{6n-9}  

c)

43n2−57n(n−3)(5n−6)\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}  

d)

8n+3nn−3+5n−6\frac{8n+3n}{n-3+5n-6}  

35.

4xx−5−3x−6\frac{4x}{x-5}-\frac{3}{x-6}  Simplify

a)

4x2−27x+15(x−6)(x−5)\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}  

b)

4x−32x+1\frac{4x-3}{2x+1}  

c)

4x2−27x+21(x−6)(x−5)\frac{4x^2-27x+21}{\left(x-6\right)\left(x-5\right)}  

d)

4x2+21x+15(x−5)(x+6)\frac{4x^2+21x+15}{\left(x-5\right)\left(x+6\right)}  

36.

2−7x2+x−302-\frac{7}{x^2+x-30}  Simplify

a)

2x2−2x−67(x−6)(x+5)\frac{2x^2-2x-67}{\left(x-6\right)\left(x+5\right)}  

b)

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

c)

−5x2+x−30\frac{-5}{x^2+x-30}  

d)

2x2+2x−67(x+6)(x−5)\frac{2x^2+2x-67}{\left(x+6\right)\left(x-5\right)}  

37.

Simplify  1n+5×n2+2n−15n−8\frac{1}{n+5}\times\frac{n^2+2n-15}{n-8}  

a)

n−3n−8\frac{n-3}{n-8}  

b)

n−3(n+5)(n−8)\frac{n-3}{\left(n+5\right)\left(n-8\right)}  

c)

n2+2n−15(n+5)(n−8)\frac{n^2+2n-15}{\left(n+5\right)\left(n-8\right)}  

d)

n2+2n−142n−3\frac{n^2+2n-14}{2n-3}  

38.

2a−206a×a−9a−10\frac{2a-20}{6a}\times\frac{a-9}{a-10}  Simplify

a)

2a2−1806a2−60a\frac{2a^2-180}{6a^2-60a}  

b)

2(a−9)6a\frac{2\left(a-9\right)}{6a}  

c)

a−93a\frac{a-9}{3a}  

d)

3a−297a−10\frac{3a-29}{7a-10}  

39.

m2+m−30m2+13m +42÷m−2m+7\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}  Simplify

a)

m−5m−2\frac{m-5}{m-2}  

b)

(m−5)(m−2)(m+7)2\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}  

c)

m2+2m−32m2+14m+49\frac{m^2+2m-32}{m^2+14m+49}  

d)

−52m2\frac{-5}{2m^2}  

40.

28m3−64m2÷18m2\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}  

a)

2m−64m2\frac{2}{m-64m^2}  

b)

16m28m2(m−8)\frac{16m^2}{8m^2\left(m-8\right)}  

c)

264m4(m−8)\frac{2}{64m^4\left(m-8\right)}  

d)

2m−8\frac{2}{m-8}  

41.

x+1x21x+x+1x\frac{\frac{x+1}{x^2}}{\frac{1}{x}+\frac{x+1}{x}}  Simplify

a)

x+1x2x+2x\frac{\frac{x+1}{x^2}}{\frac{x+2}{x}}  

b)

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

c)

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

d)

1x\frac{1}{x}  

42.

m13+18m\frac{m}{\frac{1}{3}+\frac{18}{m}}  Simplify

a)

3m2m+54\frac{3m^2}{m+54}  

b)

mm+543m\frac{m}{\frac{m+54}{3m}}  

c)

3m+54\frac{3}{m+54}  

d)

3m219\frac{3m^2}{19}  

43.

When adding rational expressions, you must add numerators together and denominators together.

a)

True

b)

False

44.

Given the sum

3xx+2+6x+1(x+2)(x−5)\frac{3x}{x+2}+\frac{6x+1}{\left(x+2\right)\left(x-5\right)}  


What is the LCD (lowest common denominator)?

a)

(x+2)(x+2)(x−5)\left(x+2\right)\left(x+2\right)\left(x-5\right)  

b)

(x+2)(x−5)\left(x+2\right)\left(x-5\right)  

c)

x−5x-5  

d)

x+2x+2  

45.

Given

(x+1)(x−7)(x−4)(x+3)\frac{\left(x+1\right)\left(x-7\right)}{\left(x-4\right)\left(x+3\right)}  

What values will make the rational expression UNDEFINED?

a)

x=−1, x=7x=-1,\ x=7  

b)

x=−1, x=4, x=7, x=−3x=-1,\ x=4,\ x=7,\ x=-3  

c)

None

d)

x=4 , x=−3x=4\ ,\ x=-3  

46.

2x+3x+7−x−4x+7=\frac{2x+3}{x+7}-\frac{x-4}{x+7}=  

a)

11  

b)

x−1x+7\frac{x-1}{x+7}  

c)

1x+7\frac{1}{x+7}  

d)

2x2−5x−12x+7\frac{2x^2-5x-12}{x+7}  

47.

Simplify x2+x−302x−10\frac{x^2+x-30}{2x-10}  

a)

x+3x+3  

b)

x2−32\frac{x^2-3}{2}  

c)

x+62x−2\frac{x+6}{2x-2}  

d)

x+62\frac{x+6}{2}  

48.

x2+10x+25x2−9⋅x2+3xx+5=\frac{x^2+10x+25}{x^2-9}\cdot\frac{x^2+3x}{x+5}=  

a)

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

b)

x(x−5)x−3\frac{x\left(x-5\right)}{x-3}  

c)

x(x+5)x−3\frac{x\left(x+5\right)}{x-3}  

d)

x(x−5)x+3\frac{x\left(x-5\right)}{x+3}  

49.

30x2+4x−12÷6xx−2=\frac{30}{x^2+4x-12}\div\frac{6x}{x-2}=  

a)

5x(x+6)\frac{5}{x\left(x+6\right)}  

b)

5x(x−6)\frac{5}{x\left(x-6\right)}  

c)

180x(x+6)(x−2)\frac{180x}{\left(x+6\right)\left(x-2\right)}  

d)

5x+6\frac{5}{x+6}  

50.

2m−n8n+6m−3n8n=\frac{2m-n}{8n}+\frac{6m-3n}{8n}=  

a)

m−1m-1  

b)

8m−4n16m2\frac{8m-4n}{16m^2}  

c)

2m−n2n\frac{2m-n}{2n}  

d)

8m+2n8n\frac{8m+2n}{8n}  

51.

x2−y22x−2y÷8x+y=\frac{x^2-y^2}{2x-2y}\div\frac{8}{x+y}=  

a)

116\frac{1}{16}  

b)

(x+y)216\frac{\left(x+y\right)^2}{16}  

c)

x+y8\frac{x+y}{8}  

d)

(x+y)(x−y)16\frac{\left(x+y\right)\left(x-y\right)}{16}  

52.

Simplify the expression x2−2x−24x2−5x−36\frac{x^2-2x-24}{x^2-5x-36}  

a)

x−6x+9\frac{x-6}{x+9}  

b)

x+6x+9\frac{x+6}{x+9}  

c)

x+6x−9\frac{x+6}{x-9}  

d)

x−6x−9\frac{x-6}{x-9}  

53.
(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)
54.
20x³/(5x+10)
a)
A.4x³/(x+2)
b)
B.4x³/(x+10)
c)
C.2x³/(5x+1)
d)
D. 2x³/(x+5)
55.
(-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)
56.
Simplify by cancelling
a)
1
b)
-1
c)
Can't be simplified
57.
Which of the following is equivalent?
(7-m)
a)
(m-7)
b)
-(m+7)
c)
-(7+m)
d)
-(m-7)
58.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
59.
Simplify.
a)
A.
b)
B.
c)
C.
d)
D.
60.
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)
61.
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)
62.

Simplify

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

a)

8/(x - 4)

b)

-x/(x - 4)

c)

-8

d)

8

63.
(4 - x2) / (x2 - x - 2)
a)
4 / (-x - 2)
b)
-2 / (-X - 1)
c)
-1(x + 2) / (x + 1)
64.
What is the excluded value: 
7 / (x - 3)
a)
7
b)
There is not one.
c)
3
65.
(5x2 + 21x + 4) / (25x + 100)
a)
(x2 + 21x + 1) / (5x + 25)
b)
5x2 + 4 / 4x + 25
c)
(5x + 1) / 25
66.
Which value of x makes the expression undefined?
a)
-2
b)
2
c)
-6
d)
-3
67.
Simplify
(2x2-98)/(2x2+18x+28)
a)
(x-7)/(x+2)
b)
(x+7)/(x+2)
c)
(x-7)/(x-2)
d)
(x+7)/(x+2)
68.
a)

A

b)

B

c)

C

d)

D

69.

Simplify: 

3x10x2+75x2\frac{3x}{10x^2}+\frac{7}{5x^2}  

a)

23x3\frac{2}{3x^3}  

b)

3x+710x2\frac{3x+7}{10x^2}  

c)

1x2\frac{1}{x^2}  

d)

3x+1410x2\frac{3x+14}{10x^2}  

70.

Simplify:

5x−3x6x2\frac{5}{x}-\frac{3x}{6x^2}  

a)

−33x2x(6x2)\frac{-33x^2}{x\left(6x^2\right)}  

b)

30−3x6x\frac{30-3x}{6x}  

c)

30x−3x6x−6x2\frac{30x-3x}{6x-6x^2}  

d)

27x6x2\frac{27x}{6x^2}  

71.

Simplify:

3x−1+56x\frac{3}{x-1}+\frac{5}{6x}  

a)

23x−56x(x−1)\frac{23x-5}{6x\left(x-1\right)}  

b)

13x−56x(x−1)\frac{13x-5}{6x\left(x-1\right)}  

c)

13x−56x2\frac{13x-5}{6x^2}  

d)

17x−617x-6  

72.

Simplify:

2x5x−3x+7\frac{2x}{5x}-\frac{3}{x+7}  

a)

2x2−x5x(x+7)\frac{2x^2-x}{5x\left(x+7\right)}  

b)

7x−215x(x+7)\frac{7x-21}{5x\left(x+7\right)}  

c)

2x2+29x5x(x+7)\frac{2x^2+29x}{5x\left(x+7\right)}  

d)

2x2−14x 5x(x+7)\frac{2x^2-14x\ }{5x\left(x+7\right)}  

73.

Simplify:

4x2x+8−12x\frac{4x}{2x+8}-\frac{12}{x}  

a)

4x2+24x−96x(2x+8)\frac{4x^2+24x-96}{x\left(2x+8\right)}  

b)

4x2−24x+96x(2x+8)\frac{4x^2-24x+96}{x\left(2x+8\right)}  

c)

4x2−24x−96x(2x+8)\frac{4x^2-24x-96}{x\left(2x+8\right)}  

d)

4x2+24x+96x(2x+8)\frac{4x^2+24x+96}{x\left(2x+8\right)}  

74.

Simplify:

5x6x2+4x−6\frac{5x}{6x^2}+\frac{4}{x-6}  

a)

29x2−30x6x2(x−6)\frac{29x^2-30x}{6x^2\left(x-6\right)}  

b)

5x2−6x6x2(x−6)\frac{5x^2-6x}{6x^2\left(x-6\right)}  

c)

−19x2−30x6x2(x−6)\frac{-19x^2-30x}{6x^2\left(x-6\right)}  

d)

no solution

75.

Simplify:

3x+4+2x−2\frac{3}{x+4}+\frac{2}{x-2}  

a)

5x+2(x+4)(x−2)\frac{5x+2}{\left(x+4\right)\left(x-2\right)}  

b)

3x−6(x−2)(x+4)\frac{3x-6}{\left(x-2\right)\left(x+4\right)}  

c)

5x−10(x−2)(x+4)\frac{5x-10}{\left(x-2\right)\left(x+4\right)}  

d)

6x+24(x−2)(x+4)\frac{6x+24}{\left(x-2\right)\left(x+4\right)}  

76.

Simplify:

5x2x−3−4x23x+1\frac{5x}{2x-3}-\frac{4x^2}{3x+1}  

a)

no solution

b)

−8x3+27x2+5x(2x−3)(3x+1)\frac{-8x^3+27x^2+5x}{\left(2x-3\right)\left(3x+1\right)}  

c)

−8x3+3x2+5x(2x−3)(3x+1)\frac{-8x^3+3x^2+5x}{\left(2x-3\right)\left(3x+1\right)}  

d)

7x2+17x(2x−3)(3x+1)\frac{7x^2+17x}{\left(2x-3\right)\left(3x+1\right)}  

77.

Simplify:

−3xx+5+72x−8\frac{-3x}{x+5}+\frac{7}{2x-8}  

a)

−6x2+31x+35(x+5)(2x−8)\frac{-6x^2+31x+35}{\left(x+5\right)\left(2x-8\right)}  

b)

−6x2−17x+35(x+5)(2x−8)\frac{-6x^2-17x+35}{\left(x+5\right)\left(2x-8\right)}  

c)

25x+35(x+5)(2x−8)\frac{25x+35}{\left(x+5\right)\left(2x-8\right)}  

d)

6x2−17x+35(x+5)(2x−8)\frac{6x^2-17x+35}{\left(x+5\right)\left(2x-8\right)}  

78.

Simplify: 

8xx−4−113x+1\frac{8x}{x-4}-\frac{11}{3x+1}  

a)

24x2−3x−44(3x+1)(x−4)\frac{24x^2-3x-44}{\left(3x+1\right)\left(x-4\right)}  

b)

24x2+19x−44(3x+1)(x−4)\frac{24x^2+19x-44}{\left(3x+1\right)\left(x-4\right)}  

c)

24x2−3x+44(3x+1)(x−4)\frac{24x^2-3x+44}{\left(3x+1\right)\left(x-4\right)}  

d)

13x2+52x(3x+1)(x−4)\frac{13x^2+52x}{\left(3x+1\right)\left(x-4\right)}  

79.

Simplify: 

6x2−5x8x\frac{6x}{2}-\frac{5x}{8x}  

a)

48x2−5x2(8x)\frac{48x^2-5x}{2\left(8x\right)}  

b)

24x2−5x8x\frac{24x^2-5x}{8x}  

c)

19x8x\frac{19x}{8x}  

d)

24x2−10x8x\frac{24x^2-10x}{8x}  

80.

Simplify: 

52x+8x12x\frac{5}{2x}+\frac{8x}{12x}  

a)

38x12x\frac{38x}{12x}  

b)

8x+3012x\frac{8x+30}{12x}  

c)

25+8x12x\frac{25+8x}{12x}  

d)

76x24x2\frac{76x}{24x^2}  

81.

Simplify: 

7x15−2x3\frac{7x}{15}-\frac{2x}{3}  

a)

17x15\frac{17x}{15}  

b)

3x15\frac{3x}{15}  

c)

19x45\frac{19x}{45}  

d)

−3x15\frac{-3x}{15}  

82.

Simplify: 

12x5x2+6x\frac{12x}{5x^2}+\frac{6}{x}  

a)

−18x25x3\frac{-18x^2}{5x^3}  

b)

18x5x2\frac{18x}{5x^2}  

c)

42x25x2\frac{42x^2}{5x^2}  

d)

42x5x2\frac{42x}{5x^2}  

83.

Simplify:
4x3x2+2x+5\frac{4x}{3x^2}+\frac{2}{x+5}  

a)

10x2+45x3x2(x+5)\frac{10x^2+45x}{3x^2\left(x+5\right)}  

b)

6x2+24x3x2(x+5)\frac{6x^2+24x}{3x^2\left(x+5\right)}  

c)

10x2+20x3x2(x+5)\frac{10x^2+20x}{3x^2\left(x+5\right)}  

d)

4x2+26x3x2(x+5)\frac{4x^2+26x}{3x^2\left(x+5\right)}  

84.

Simplify: 

62x+3−8x−1\frac{6}{2x+3}-\frac{8}{x-1}  

a)

−10x+18(x−1)(2x+3)\frac{-10x+18}{\left(x-1\right)\left(2x+3\right)}  

b)

−10x−30(x−1)(2x+3)\frac{-10x-30}{\left(x-1\right)\left(2x+3\right)}  

c)

22x+18(x−1)(2x+3)\frac{22x+18}{\left(x-1\right)\left(2x+3\right)}  

d)

22x+30(x−1)(2x+3)\frac{22x+30}{\left(x-1\right)\left(2x+3\right)}  

85.
a)
A
b)
B
c)
C
d)
D
86.
a)
A
b)
B
c)
C
d)
D
87.
a)
A
b)
B
c)
C
d)
D
88.

Add

2x−34x−7+2x−34x−7\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}  

a)

4x−64x−7 , x≠−74\frac{4x-6}{4x-7}\ ,\ x\ne-\frac{7}{4}  

b)

4x2−6x+94x−7 ,  x≠74\frac{4x^2-6x+9}{4x-7}\ ,\ \ x\ne\frac{7}{4}  

c)

4x−64x−7  , x≠74\frac{4x-6}{4x-7\ }\ ,\ x\ne\frac{7}{4}

d)

An 4x−68x−14, x≠148\frac{4x-6}{8x-14},\ x\ne\frac{14}{8}  swer 4

89.

Subtract
x−53x+4−3x−53x+4\frac{x-5}{3x+4}-\frac{3x-5}{3x+4}  

a)

−2x−103x+4; x≠−43\frac{-2x-10}{3x+4};\ x\ne-\frac{4}{3}  

b)

−2x3c+4; x≠−43\frac{-2x}{3c+4};\ x\ne-\frac{4}{3}  

c)

−2x; x≠0-2x;\ x\ne0  

d)

−2x−10; x≠0-2x-10;\ x\ne0  

90.

Add
3x−2x+2+2x4x−1\frac{3x-2}{x+2}+\frac{2x}{4x-1}  

a)

14x2−7x+2(x+2)(4x−1); x≠−2, 14\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}  

b)

14x2−9x−2(x+2)(4x−1); x≠−2, 1\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ 1  

c)

12x2−7x+2(x+2)(4x−1); x≠−2, 14\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}  

d)

14x2−7x+2(x+2)(4x−1); x≠−14, 2\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-\frac{1}{4},\ 2  

91.

Subtract
x2x+3−2x+12x−3\frac{x}{2x+3}-\frac{2x+1}{2x-3}  

a)

−2x2−11x−3(2x−3)(2x+3); x≠±23\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{2}{3}  

b)

−2x2−11x−3(2x−3)(2x+3); x≠±32\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{3}{2}  

c)

−2x2+5x+3(2x−3)(2x+3); x≠±32\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{3}{2}  

d)

−2x2+5x+3(2x−3)(2x+3); x≠±23\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)};\ x\ne\pm\frac{2}{3}  

92.

Subtract
6x2+4x−32−x−5x−4\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}  

a)

−x2+3x−34(x+8)(x−4); x≠−8, 4\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4  

b)

−x2+3x−34(x+8)(x−4); x≠−4, 8\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8  

c)

−x2−3x+46(x+8)(x−4); x≠−8, 4\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4  

d)

−x2−3x+46(x+8)(x−4); x≠−4, 8\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8  

93.

Subtract
x2−32x+7−2x−52x+7\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}  

a)

x2−2x−82x+7; x≠−72\frac{x^2-2x-8}{2x+7};\ x\ne-\frac{7}{2}  

b)

x2−2x−8; x≠0x^2-2x-8;\ x\ne0  

c)

x2−2x+2; x≠0x^2-2x+2;\ x\ne0  

d)

x2−2x+22x+7; x≠−72\frac{x^2-2x+2}{2x+7};\ x\ne-\frac{7}{2}  

94.

Simplify (add & divide)
12x+23xx−1x−3\frac{\frac{1}{2x}+\frac{2}{3x}}{\frac{x-1}{x-3}}  

a)

7x−216x2−6x; x≠0, 1, 3\frac{7x-21}{6x^2-6x};\ x\ne0,\ 1,\ 3  

b)

7x−216x2−6x; x≠1, 3\frac{7x-21}{6x^2-6x};\ x\ne1,\ 3  

c)

7x2−21x6x3−6x2; x≠0, 1, 3\frac{7x^2-21x}{6x^3-6x^2};\ x\ne0,\ 1,\ 3  

d)

7x2−21x6x3−6x2; x≠1, 3\frac{7x^2-21x}{6x^3-6x^2};\ x\ne1,\ 3  

95.

Add
7xx2−5x+x2x−5\frac{7x}{x^2-5x}+\frac{x^2}{x-5}  

a)

x3+7xx(x−5); x≠5\frac{x^3+7x}{x\left(x-5\right)};\ x\ne5  

b)

x2+7x−5; x≠0, 5\frac{x^2+7}{x-5};\ x\ne0,\ 5  

c)

x4−5x3+7x2−35x(x2−5x)(x−5); x≠5\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)};\ x\ne5  

d)

x4−5x3+7x2−35x(x2−5x)(x−5); x≠0, 5\frac{x^4-5x^3+7x^2-35x}{\left(x^2-5x\right)\left(x-5\right)};\ x\ne0,\ 5  

96.

Add
2x−34x−7+2x−34x−7\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}  

a)

4x−64x−7; x≠−74\frac{4x-6}{4x-7};\ x\ne-\frac{7}{4}  

b)

4x2−6x+94x−7; x≠74\frac{4x^2-6x+9}{4x-7};\ x\ne\frac{7}{4}  

c)

4x−64x−7; x≠74\frac{4x-6}{4x-7};\ x\ne\frac{7}{4}  

d)

4x−68x−14; x≠−148\frac{4x-6}{8x-14};\ x\ne-\frac{14}{8}  

97.

Add
2xx2−36+x+4x+6\frac{2x}{x^2-36}+\frac{x+4}{x+6}  

a)

x2−24(x+6)(x−6); x≠±6\frac{x^2-24}{\left(x+6\right)\left(x-6\right)};\ x\ne\pm6  

b)

x3+6x2−24x(x+6)(x2−36); x≠−6, 36\frac{x^3+6x^2-24x}{\left(x+6\right)\left(x^2-36\right)};\ x\ne-6,\ 36  

c)

x2+2x−24(x+6)(x−6); x≠±6\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)};\ x\ne\pm6  

d)

x2+12x+24(x+6)(x−6); x≠±6\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)};\ x\ne\pm6  

98.

Add
2x2−x−20+3x2+7x+12\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}  

a)

5x−9(x−5)(x+4)(x+3); x≠−5, 3 4\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-5,\ 3\ 4  

b)

5x−11(x−5)(x+4)(x+3); x≠−4,−3, 5\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-4,-3,\ 5  

c)

5x−11(x−5)(x+4)(x+3); x≠−5, 3 4\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-5,\ 3\ 4  

d)

5x−9(x−5)(x+4)(x+3); x≠−4,−3 5\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)};\ x\ne-4,-3\ 5  

99.
Find the least common denominator of the expression
a)
18
b)
6x
c)
3xy
d)
6xy
100.

Find the LCD of the following rational expressions
2xx+1\frac{2x}{x+1}  and  1x2−1\frac{1}{x^2-1}

a)

(x+1)(x-1)

b)

(x+1)2 (x-1)

c)

(2x+2)

101.
Find the LCD of these fractions.
a)
(x+2)(x-2)
b)
(x+2)(x+1)
c)
(x+2)(x-2)(x+1)
d)
(x-2)(x+1)
102.
Find the LCD of these fractions.
a)
(x+2)(x-2)
b)
(x+2)
c)
(x-2)
d)
(x2-4)(x+2)
103.
Simplify the expression
a)
6x / 20xy
b)
3 / 10y
c)
(6x+1) / (20xy)
d)
3 / 20xy
104.
Simplify the expression
a)
n / 2m 
b)
n / 3m 
c)
(m2 + 4n2) / 12m
d)
n / 4m 
105.

Simplify the expression

a)

(-17x - 12y) / 15x

b)

(23x - 4y) / 15x

c)

(-17x - 4y) / 15x

d)

(-3x - 4y) / 8x

106.
a)
A
b)
B
c)
C
d)
D
107.
a)
b)
c)
d)
108.
Simplify the expression
a)
(12n2 + 28n + 4) / (2n-5)(n+2)
b)
(12n2 - 28n + 4) / (2n-5)(n+2)
c)
(8n) / (3n + 3)
d)
(12n2 + 2n -3) / (2n-5)(n+2)
109.
SIMPLIFY
a)
A
b)
B
c)
C
d)
D
110.

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),

111.

Find the product

a)

A

b)

B

c)

C

d)

D

112.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

113.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

114.

Simplify

a)

A

b)

B

c)

C

d)

D

115.
Simplify. 
a)
A
b)
B
c)
C
d)
D
116.
Simplify. 
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
117.
a)

1 / 5p

b)

12 / 50p

c)

2 / 10p

d)

8 / 16p

118.
a)

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

b)

(r - 8) / (r + 2)

c)

(r + 2) / 7

d)

(r - 8) / 7

119.

Find the product

a)

A

b)

B

c)

C

d)

D

120.
Simplify. 
a)
(m+6)/(m-3)
b)
7/(m-3)
c)
7(m+6)
d)
(m-3)
121.
Simplify. 
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
122.
Simplify.
a)
1/(n-7)
b)
n-7
c)
(n-6)/(n-7)
d)
n-6
123.
(X2 + X - 20) / (X2 + 2X - 15)
a)
(X - 4) / (2X - 3)
b)
(X - 4) / (X - 3)
c)
(X +4) / (X + 3)
124.

Simplify completely. State any restrictions.

a)
b)
c)
d)
125.

Simplify completely. State any restrictions.

a)
b)
c)
d)
126.

Simplify the rational expression.


9 - x

---------

x2 - 81

a)

1

-------

x + 9

b)

-1

-------

x + 9

c)

x + 9

d)

-1

-------

x - 9

127.
Divide and Simplify
a)
1/6
b)
x+10/ 6x+60
c)
x+8/ 6x+60 
d)
(x+10)(x+8)/ 6x+60
128.
Simplify. 
a)
A
b)
B
c)
C
d)
D
129.
Simplify. 
a)
A
b)
B
c)
C
d)
D
130.
Simplify. 
a)
A
b)
B
c)
C
d)
D
131.
a)

7v2(v + 1) / 10

b)

(v + 1)

c)

1 / 10

d)

(v + 1) / 10

132.

Simplify

a)

A

b)

B

c)

C

d)

D

133.

Simplify.

a)

A

b)

B

c)

C

d)

D

134.
Simplify and state the excluded values.
a)
A
b)
B
c)
C
d)
D
135.

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),

136.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

137.

Simplify.

a)

A

b)

B

c)

C

d)

D

138.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

139.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

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

140.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

141.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

142.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

143.
Divide the rational expressions:
a)
A.
b)
B.
c)
C.
d)
D.
144.

SIMPLIFY

a)

A

b)

B

c)

C

d)

D

145.
Simplify. 
a)
(x+6)/(x+4)
b)
(x+6)(x+4)
c)
(x+6)
d)
(x+6)/(x-5)
146.
SIMPLIFY
a)
A
b)
B
c)
C
d)
D
147.
SIMPLIFY
a)
A
b)
B
c)
C
d)
D
148.
SIMPLIFY
a)
A
b)
B
c)
C
d)
D
149.
Simplify
a)
(x-9)/(x+9)
b)
1/(x-9)
c)
(x+9)
d)
1/(x+9)
150.

Find the product

a)

A

b)

B

c)

C

d)

D

151.

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),

152.
a)

1

b)

(x - 8) / (x + 5)

c)

(x - 5) / (x + 5)

d)

(x + 1) / (x + 5)

153.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

154.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

155.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

156.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

157.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

158.

Divide the Rational Expression

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

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

159.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

160.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

161.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

162.

Simplify

a)

A

b)

B

c)

C

d)

D

163.
Simplify. 
a)
A
b)
B
c)
C
d)
D
164.
a)
A
b)
B
c)
C
d)
D

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