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Worksheets

FRACTIONS -gr 10

Total questions: 125

Worksheet time: 6hrs 15mins

Name
Class
Date
1.

Solve:

2x+44=2\frac{2x+4}{4}=2  

a)

x=2x=2  

b)

x=−4x=-4  

c)

x=0x=0  

d)

x=−2x=-2  

2.

Solve:

6a−12=4\frac{6a-1}{2}=4  

a)

a=1.67a=1.67  

b)

a=1a=1  

c)

a=1.5a=1.5  

d)

a=2a=2  

3.

Solve:

x−83=−10\frac{x-8}{3}=-10  

a)

x=38x=38  

b)

x=−6x=-6  

c)

x=−22x=-22  

d)

x=−38x=-38  

4.

Solve:

5h−42=18\frac{5h-4}{2}=18  

a)

h=6.4h=6.4  

b)

h=2.6h=2.6  

c)

h=9h=9  

d)

h=8h=8  

5.

Solve:

15+9a6=7\frac{15+9a}{6}=7  

a)

a=43a=\frac{4}{3}  

b)

h=3h=3  

c)

a=193a=\frac{19}{3}  

d)

h=−4h=-4  

6.

Solve:

7m+32−1=18\frac{7m+3}{2}-1=18  

a)

m=5m=5  

b)

m=347m=\frac{34}{7}  

c)

m=327m=\frac{32}{7}  

d)

m=7m=7  

7.

Solve:

4(d+16)2=24\frac{4\left(d+16\right)}{2}=24  

a)

d=32d=32  

b)

d=4d=4  

c)

d=−4d=-4  

d)

d=−32d=-32  

8.

Solve:

−8−3k2−5=6\frac{-8-3k}{2}-5=6  

a)

k=−143k=-\frac{14}{3}  

b)

k=2k=2  

c)

k=−10k=-10  

d)

k=−253k=-\frac{25}{3}  

9.

Solve:

6+3m+18=56+\frac{3m+1}{8}=5  

a)

m=−3m=-3  

b)

m=11m=11  

c)

m=3m=3  

d)

m=6m=6  

10.

Solve:

−40+4w9+4=0\frac{-40+4w}{9}+4=0  

a)

w=9w=9  

b)

w=1w=1  

c)

w=10w=10  

d)

w=−11w=-11  

11.

Find the value of the unknown variable

a)

A

b)

B

c)

C

d)

D

12.

Find the value of the unknown variable

a)

A

b)

B

c)

C

d)

D

13.
Solve for x.
a)
55
b)
60
c)
15
d)
35
14.

Solve:

a)

50

b)

10

c)

-10

d)

-50

15.

Solve:

a)

35

b)

-84

c)

30

d)

23

16.

Solve:
2x−34=9\frac{2x-3}{4}=9  

a)

x = 24

b)

x = 12

c)

x = 17.5

d)

x = 19.5

17.

Solve:

a)

8

b)

6

c)

54

d)

50

18.

Solve:

a)

x = 15

b)

x = 40

c)

x = 48

d)

x = 37

19.
Solve for v.
a)
60
b)
-3
c)
15
d)
3
20.

Solve:
9 + a−27=−1\frac{9\ +\ a}{-27}=-1  

a)

a = -36

b)

a = 18

21.

Solve:
13(6y−9)=11\frac{1}{3}\left(6y-9\right)=11  

a)

y = 9

b)

y = -9

c)

y = 7

d)

y = -7

22.

Solve:

  −27x−6=2-\frac{2}{7}x-6=2  

a)

X = -28

b)

X = 28

c)

X = -14

d)

X = 14

23.

Solve:
x8+10=11\frac{x}{8}+10=11  

a)

x = -8

b)

x = 8

24.

3p+41−p\frac{3}{p}+\frac{4}{1-p}  

a)

3+4p1−p\frac{3+4p}{1-p}  

b)

3+p1−p\frac{3+p}{1-p}  

c)

3+pp(1−p)\frac{3+p}{p\left(1-p\right)}  

d)

3+4p23+4p^2  

25.

Express p+2q2pq−p+1p\frac{p+2q}{2pq}-\frac{p+1}{p}  as a single fraction in its simplest form

a)

1−2q2q\frac{1-2q}{2q}  

b)

p−2pq2pq\frac{p-2pq}{2pq}  

c)

p−2pq+4q2pq\frac{p-2pq+4q}{2pq}  

d)

p−2pq−4q2pq\frac{p-2pq-4q}{2pq}  

26.

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),

27.

Simplify  8x2+10x−32x2−7x−15\frac{8x^2+10x-3}{2x^2-7x-15} .

a)

4x−1x−5\frac{4x-1}{x-5}  

b)

2x+3x−5\frac{2x+3}{x-5}  

c)

4x−12x+3\frac{4x-1}{2x+3}  

d)

4x+1x+5\frac{4x+1}{x+5}  

28.

Simplify  6x2+3x4x2−1\frac{6x^2+3x}{4x^2-1} . 

a)

3x2x−1\frac{3x}{2x-1}  

b)

2x+12x−1\frac{2x+1}{2x-1}  

c)

3x2x+1\frac{3x}{2x+1}  

d)

−3x2x+1-\frac{3x}{2x+1}  

29.

Simplify x2+6x+9x2−9\frac{x^2+6x+9}{x^2-9} .

a)

x+3x−3\frac{x+3}{x-3}  

b)

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

c)

x−3x+3\frac{x-3}{x+3}  

d)

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

30.

x2+6x+9x2−2x−15\frac{x^2+6x+9}{x^2-2x-15}  

a)

x+3x+5\frac{x+3}{x+5}  

b)

x+5x−3\frac{x+5}{x-3}  

c)

x−5x+3\frac{x-5}{x+3}  

d)

x+3x−5\frac{x+3}{x-5}  

31.

x2+5x+4x2+4x+3\frac{x^2+5x+4}{x^2+4x+3}  

a)

x+4x+3\frac{x+4}{x+3}  

b)

x+1x+3\frac{x+1}{x+3}  

c)

x+4x+1\frac{x+4}{x+1}  

d)

x+3x+4\frac{x+3}{x+4}  

32.

33a2b244a3b\frac{33a^2b^2}{44a^3b}  

a)

3ab4ab\frac{3ab}{4ab}  

b)

3b4a\frac{3b}{4a}  

c)

3ab4\frac{3ab}{4}  

d)

34ab\frac{3}{4ab}  

33.
Simplify the algebraic fraction.
a)
-m
b)

−1m\frac{-1}{m}  

c)

mn\frac{m}{n}  

d)

1mn\frac{1}{mn}  

34.

6−3x2x2−8÷12x−486x+12\frac{6-3x}{2x^2-8}\div\frac{12x-48}{6x+12}  

a)

3x−4\frac{3}{x-4}  

b)

34(x−4)\frac{3}{4\left(x-4\right)}  

c)

−34(x−4)\frac{-3}{4\left(x-4\right)}  

d)

none of the above

35.

Multiply the two rational expressions and simplify the result:

x2−4x+4x2−5x⋅xx2−2x\frac{x^2-4x+4}{x^2-5x}\cdot\frac{x}{x^2-2x}  

a)

x−2x−5x\frac{x-2}{x-5x}  

b)

x−2x2−5x\frac{x-2}{x^2-5x}  

c)

x−2x−5\frac{x-2}{x-5}  

d)

x−4x2−5x\frac{x-4}{x^2-5x}  

36.

Multiply the two rational expressions and simplify the result:

x2−4x2−9⋅x−3x+2\frac{x^2-4}{x^2-9}\cdot\frac{x-3}{x+2}  

a)

x−2x+3\frac{x-2}{x+3}  

b)

x+2x−3\frac{x+2}{x-3}  

c)

−23-\frac{2}{3}  

d)

x−2x−3\frac{x-2}{x-3}  

37.

Multiply the two rational expressions and simplify the result:

x2−5x+6x2−4⋅x2−3x+2x2−9\frac{x^2-5x+6}{x^2-4}\cdot\frac{x^2-3x+2}{x^2-9}  

a)

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

b)

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

c)

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

d)

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

38.

16x2−4(3x2)(2yz)÷4(2x+1)29xz\frac{16x^2-4}{\left(3x^2\right)\left(2yz\right)}\div\frac{4\left(2x+1\right)^2}{9xz}  

a)

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

b)

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

c)

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

d)

none of the above

39.

Simplify: x2−6xx2−36÷x2x+6\frac{x^2-6x}{x^2-36}\div\frac{x^2}{x+6}  

a)
1/x2
b)
x
c)
1/x
d)
x2
40.

Simplify: y2−7y+10y2−y−2÷y2−2y−15y2+5y+4\frac{y^2-7y+10}{y^2-y-2}\div\frac{y^2-2y-15}{y^2+5y+4}  

a)

y−4y−3\frac{y-4}{y-3}  

b)

y+4y+3\frac{y+4}{y+3}  

c)

y+3y+4\frac{y+3}{y+4}  

d)

y−3y−4\frac{y-3}{y-4}  

41.
Simplify the algebraic fraction.
a)
1/a
b)
8a/9
c)
9/8a
d)
9a/8
42.
Simplify the algebraic fraction.
a)
-3/b
b)
-b/3
c)
3b
d)
-3b
43.
a)
2a/0
b)
2a/5
c)
2a/10
d)
2a
44.
Simplify the algebraic fraction.
a)
1/a
b)
8a/9
c)
9/8a
d)
9a/8
45.
Simplify the algebraic fraction.
a)
6/xy(1+2x)
b)
(1+2x)/6xy
c)
xy/6(1-2x)
d)
y/6x(1-2x)
46.

3x−4+x2x+7\frac{3}{x-4}+\frac{x}{2x+7}  

a)

x2+2x+21(x−4)(2x+7)\frac{x^2+2x+21}{\left(x-4\right)\left(2x+7\right)}  

b)

x2+6x+21(x−4)(2x+7)\frac{x^2+6x+21}{\left(x-4\right)\left(2x+7\right)}  

c)

x2+6x+7(x−4)(2x+7)\frac{x^2+6x+7}{\left(x-4\right)\left(2x+7\right)}  

d)

x2+2x+7(x−4)(2x+7)\frac{x^2+2x+7}{\left(x-4\right)\left(2x+7\right)}  

47.

23x2−16x+2x+4\frac{2}{3x^2}-\frac{1}{6x}+\frac{2}{x+4}  

a)

11x2+166x2(x+4)\frac{11x^2+16}{6x^2\left(x+4\right)}  

b)

11x2+8x+46x2(x+4)\frac{11x^2+8x+4}{6x^2\left(x+4\right)}  

c)

13x2+166x2(x+4)\frac{13x^2+16}{6x^2\left(x+4\right)}  

d)

13x2+8x+46x2(x+4)\frac{13x^2+8x+4}{6x^2\left(x+4\right)}  

48.

xx2+12x+36−x−8x+6\frac{x}{x^2+12x+36}-\frac{x-8}{x+6}  

a)

−x2+3x+48(x+6)2\frac{-x^2+3x+48}{\left(x+6\right)^2}  

b)

−x2−x−48(x+6)2\frac{-x^2-x-48}{\left(x+6\right)^2}  

c)

x2−x−48(x+6)2\frac{x^2-x-48}{\left(x+6\right)^2}  

d)

−8x+48(x+6)2-\frac{8x+48}{\left(x+6\right)^2}  

49.

1x2−13x+42+x+1x−6−xx−7\frac{1}{x^2-13x+42}+\frac{x+1}{x-6}-\frac{x}{x-7}  

a)

−6(x−6)(x−7)-\frac{6}{\left(x-6\right)\left(x-7\right)}  

b)

2(x2+6x−3)(x−6)(x−7)\frac{2\left(x^2+6x-3\right)}{\left(x-6\right)\left(x-7\right)}  

c)

−x2+8x−6(x−6)(x−7)\frac{-x^2+8x-6}{\left(x-6\right)\left(x-7\right)}  

d)

x2−4x−6(x−6)(x−7)\frac{x^2-4x-6}{\left(x-6\right)\left(x-7\right)}  

50.

x+10(3x+8)2+x3x+8\frac{x+10}{\left(3x+8\right)^2}+\frac{x}{3x+8}  

a)

3x2+9x+10(3x+8)2\frac{3x^2+9x+10}{\left(3x+8\right)^2}  

b)

 3x2+x+18(3x+8)2\ \frac{3x^2+x+18}{\left(3x+8\right)^2}  

c)

2(x+5)(3x+8)2\frac{2\left(x+5\right)}{\left(3x+8\right)^2}  

d)

x2+x+10(3x+8)2\frac{x^2+x+10}{\left(3x+8\right)^2}  

51.

23x+1−15x+3 \frac{2}{3x+1}-\frac{1}{5x+3}\  

a)

7x+5(3x+1)(5x+3)\frac{7x+5}{\left(3x+1\right)\left(5x+3\right)}  

b)

7x+4(3x+1)(5x+3)\frac{7x+4}{\left(3x+1\right)\left(5x+3\right)}  

c)

13x+7(3x+1)(5x+3)\frac{13x+7}{\left(3x+1\right)\left(5x+3\right)}  

d)

7x+2(3x+1)(5x+3)\frac{7x+2}{\left(3x+1\right)\left(5x+3\right)}  

52.

3x+1+x+4(x+1)(x+2)\frac{3}{x+1}+\frac{x+4}{\left(x+1\right)\left(x+2\right)}  

a)

2(2x+5)(x+1)(x+2)\frac{2\left(2x+5\right)}{\left(x+1\right)\left(x+2\right)}  

b)

 4x+6(x+1)(x+2)\ \frac{4x+6}{\left(x+1\right)\left(x+2\right)}  

c)

x+7(x+1)(x+2)\frac{x+7}{\left(x+1\right)\left(x+2\right)}  

d)

2(x+5)(x+1)(x+2)\frac{2\left(x+5\right)}{\left(x+1\right)\left(x+2\right)}  

53.

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

a)

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

b)

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

c)

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

d)

6x−1(x−1)(x−2)\frac{6x-1}{\left(x-1\right)\left(x-2\right)}  

54.

x2(x+y)(x−3y)−x−yx−3y\frac{x^2}{\left(x+y\right)\left(x-3y\right)}-\frac{x-y}{x-3y}  

a)

y2(x+y)(x−3y)\frac{y^2}{\left(x+y\right)\left(x-3y\right)}  

b)

−y2(x+y)(x−3y)-\frac{y^2}{\left(x+y\right)\left(x-3y\right)}  

c)

2x2+y2(x+y)(x−3y)\frac{2x^2+y^2}{\left(x+y\right)\left(x-3y\right)}  

d)

2x2−y2(x+y)(x−3y)\frac{2x^2-y^2}{\left(x+y\right)\left(x-3y\right)}  

55.

3xx−3−xx2−9\frac{3x}{x-3}-\frac{x}{x^2-9}  

a)

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

b)

3x2−x+9(x−3)(x+3)\frac{3x^2-x+9}{\left(x-3\right)\left(x+3\right)}  

c)

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

d)

3x2+x+9(x−3)(x+3)\frac{3x^2+x+9}{\left(x-3\right)\left(x+3\right)}  

56.

xx2−4−1x+2\frac{x}{x^2-4}-\frac{1}{x+2}  

a)

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

b)

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

c)

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

d)

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

57.

x+2x2−1−32(x−1)\frac{x+2}{x^2-1}-\frac{3}{2\left(x-1\right)}  

a)

−12(x+1)-\frac{1}{2\left(x+1\right)}  

b)

12(x+1)\frac{1}{2\left(x+1\right)}  

c)

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

d)

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

58.

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

a)

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

b)

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

c)

x+32\frac{x+3}{2}  

d)

x+32(x+2)\frac{x+3}{2\left(x+2\right)}  

59.

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

a)

(x−1)2x2\frac{\left(x-1\right)^2}{x^2}  

b)

(x+2)2x2\frac{\left(x+2\right)^2}{x^2}  

c)

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

d)

44  

60.

Combine over a common denominator:

x3+x4\frac{x}{3}+\frac{x}{4}  

a)

2x7\frac{2x}{7}  

b)

x27\frac{x^2}{7}  

c)

7x12\frac{7x}{12}  

d)

7x24\frac{7x}{24}  

61.

Combine over a common denominator:

x2+52\frac{x}{2}+\frac{5}{2}  

a)

5x2\frac{5x}{2}  

b)

x+52\frac{x+5}{2}  

c)

x+54\frac{x+5}{4}  

62.

Combine over a common denominator:

2x3−x4\frac{2x}{3}-\frac{x}{4}  

a)

5x12\frac{5x}{12}  

b)

x7\frac{x}{7}  

c)

x12\frac{x}{12}  

d)

11x12\frac{11x}{12}  

63.

Combine over a common denominator:

2x9+5x6\frac{2x}{9}+\frac{5x}{6}  

a)

7x18\frac{7x}{18}  

b)

10x9\frac{10x}{9}  

c)

7x15\frac{7x}{15}  

d)

19x18\frac{19x}{18}  

64.

Combine over a common denominator:

2x3+4x\frac{2x}{3}+\frac{4}{x}  

a)

2x+43x\frac{2x+4}{3x}  

b)

2x2+123x\frac{2x^2+12}{3x}  

c)

2x+123x\frac{2x+12}{3x}  

d)

14x3\frac{14x}{3}  

65.

Combine over a common denominator:

14x+32\frac{1}{4x}+\frac{3}{2}  

a)

46x\frac{4}{6x}  

b)

44x\frac{4}{4x}  

c)

1+6x4x\frac{1+6x}{4x}  

d)

7x4x\frac{7x}{4x}  

66.

Combine over a common denominator:

58x−12x\frac{5}{8x}-\frac{1}{2x}  

a)

46x\frac{4}{6x}  

b)

18x\frac{1}{8x}  

c)

98x\frac{9}{8x}  

d)

5−4x8x\frac{5-4x}{8x}  

67.

Combine over a common denominator:

x2−x5\frac{x}{2}-\frac{x}{5}  



(a)  

68.

Combine over a common denominator:

12x−29x\frac{1}{2x}-\frac{2}{9x}  



(a)  

69.
Simplify. 
a)
(m+6)/(m-3)
b)
7/(m-3)
c)
7(m+6)
d)
(m-3)
70.

Simplify the following.

6t5÷34t\frac{6t}{5}\div\frac{3}{4t}  

a)

8t25\frac{8t^2}{5}  

b)

18t20t\frac{18t}{20t}  

c)

9t10t\frac{9t}{10t}  

d)

10t8\frac{10t}{8}  

71.

Simplify the following.

5q7÷9q8\frac{5q}{7}\div\frac{9q}{8}  

a)

4063\frac{40}{63}  

b)

14q15\frac{14q}{15}  

c)

103q56\frac{103q}{56}  

d)

45q56\frac{45q}{56}  

72.
Solve the equation.
a)
u = 1.5
b)
u = 2
c)
u = 0
d)
u = 4
73.
Solve the equation.
a)
x = -73/11
b)
v = -73
c)
v = -73/11
d)
v = 73/11
74.
Solve the equation.
a)
q = -46
b)
q =-5
c)
q = -9.2
d)
q = -9.5
75.
Solve for x
a)
6
b)
17/5
c)
19/2
d)
- 6
76.
Solve for v
a)
- 7/6
b)
- 9/5
c)
9/5
d)
-3
77.
Solve for x
a)
5
b)
4/5
c)
1
d)
- 4
78.
Solve for x
a)
5/3, 1
b)
- 5, 1
c)
5, 2/3
d)
5, 1
79.
Solve for n
a)
- 2, - 1
b)
- 5, - 1
c)
- 2
d)
- 2, - 2/3
80.
Solve for x
a)
x = -3
b)
x = -3, 5
c)
x = 3, 5
d)
x = 5
81.

2n+16n−8=12n−16−12\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}  

a)

−235-\frac{23}{5}  

b)

77  

c)

−4-4  

d)

43\frac{4}{3}  

82.

7x−49x2+8x+12=3x+6+1x+2\frac{7x-49}{x^2+8x+12}=\frac{3}{x+6}+\frac{1}{x+2}  

a)

−2-2  

b)

55  

c)

66  

d)

613\frac{61}{3}  

83.

n−2n+3=1n2+7n+12+n+8n+4\frac{n-2}{n+3}=\frac{1}{n^2+7n+12}+\frac{n+8}{n+4}  

a)

3, 43,\ 4  

b)

33  

c)

3, 73,\ 7  

d)

−113-\frac{11}{3}  

84.

x−5x+1x2+2x=x−8x+2\frac{x-5}{x}+\frac{1}{x^2+2x}=\frac{x-8}{x+2}  

a)

95, 318\frac{9}{5},\ \frac{31}{8}  

b)

95\frac{9}{5}  

c)

318\frac{31}{8}  

d)

−7, 318-7,\ \frac{31}{8}  

85.

1b2−9b+18+b−7b−3=1b−3\frac{1}{b^2-9b+18}+\frac{b-7}{b-3}=\frac{1}{b-3}  

a)

−2, 0-2,\ 0  

b)

0, 750,\ \frac{7}{5}  

c)

77  

d)

00  

86.

1a+1=4a+12a2+a+1a\frac{1}{a+1}=\frac{4a+12}{a^2+a}+\frac{1}{a}  

a)

−134-\frac{13}{4}  

b)

−7, 1-7,\ 1  

c)

−1-1  

d)

77  

87.

5k+7=1k+3+2k−2k2+10k+21\frac{5}{k+7}=\frac{1}{k+3}+\frac{2k-2}{k^2+10k+21}  

a)

22  

b)

11  

c)

−5-5  

d)

55  

88.

n−6n2−11n+28+6n−4=n+3n2−11n+28\frac{n-6}{n^2-11n+28}+\frac{6}{n-4}=\frac{n+3}{n^2-11n+28}  

a)

32\frac{3}{2}  

b)

−172-\frac{17}{2}  

c)

44  

d)

172\frac{17}{2}  

89.

1x+8=13x+24+13\frac{1}{x+8}=\frac{1}{3x+24}+\frac{1}{3}  

a)

3, 83,\ 8  

b)

−6-6  

c)

76\frac{7}{6}  

d)

33  

90.

1x+3=3x+2−7x2+5x+6\frac{1}{x+3}=\frac{3}{x+2}-\frac{7}{x^2+5x+6}  

a)

0, 80,\ 8  

b)

00  

c)

88  

d)

33  

91.

Solve for x:  53−2x=8x\frac{5}{3}-\frac{2}{x}=\frac{8}{x}  

a)

2

b)

18/5

c)

26/5

d)

6

92.

Solve the equation for x: 2x+2+5x −2=6x2−4\frac{2}{x+2}+\frac{5}{x\ -2}=\frac{6}{x^2-4}  

a)

7

b)

6

c)

14

d)

0

93.

Solve for x:  5x−2+x−6x2−2x=1x\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}  

a)

x = 5

b)

x = 45\frac{4}{5}

c)

x = 1

d)

x = - 4

94.

Solve: 2x−2−1x+1=2x2−x−2\frac{2}{x-2}-\frac{1}{x+1}=\frac{2}{x^2-x-2}  

a)

x = 2

b)

x = -2

c)

x = 6

d)

x = 3

95.

Solve x−23x=13x+2\frac{x-2}{3x}=\frac{1}{3x}+2  

a)

0

b)

−35-\frac{3}{5}  

c)

-2

d)

−15-\frac{1}{5}  

96.

Solve x−23x=13x+2\frac{x-2}{3x}=\frac{1}{3x}+2  

a)

0

b)

−35-\frac{3}{5}  

c)

-2

d)

−15-\frac{1}{5}  

97.

Solve for y y+23−y−14=23\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}  

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

98.

1x+3=3x+2−7x2+5x+6\frac{1}{x+3}=\frac{3}{x+2}-\frac{7}{x^2+5x+6}  

a)

5

b)

00  

c)

88  

d)

33  

99.

For what value(s) of mm  is the expression  m2−2m+12m2+m−3\frac{m^2-2m+1}{2m^2+m-3}  undefined?

a)

−32, 0, 1-\frac{3}{2},\ 0,\ 1  

b)

−1, 32-1,\ \frac{3}{2}  

c)

−32, 1-\frac{3}{2},\ 1  

d)

32\frac{3}{2}  

100.

Simplify the following expression: x2+5x+4x2+2x+1×2x+2x+4\frac{x^2+5x+4}{x^2+2x+1}\times\frac{2x+2}{x+4}  

a)

12\frac{1}{2}  

b)

22  

c)

(x+4)22(x+1)2\frac{\left(x+4\right)^2}{2\left(x+1\right)^2}  

d)

x+42(x+1)\frac{x+4}{2\left(x+1\right)}  

101.

Simplify the following expression:
a+b3÷a2+b212\frac{a+b}{3}\div\frac{a^2+b^2}{12}  

a)

a+b4(a2+b2)\frac{a+b}{4\left(a^2+b^2\right)}  

b)

4a+b\frac{4}{a+b}  

c)

a+b4\frac{a+b}{4}  

d)

4(a+b)a2+b2\frac{4\left(a+b\right)}{a^2+b^2}  

102.

Solve nn−4+n=12−4nn−4\frac{n}{n-4}+n=\frac{12-4n}{n-4}  

a)

n=−4, n=3n=-4,\ n=3  

b)

n=−3, n=4n=-3,\ n=4  

c)

n=−4n=-4  

d)

n=3n=3  

103.

Solve the following equation for x:
12x+34=32\frac{12}{x}+\frac{3}{4}=\frac{3}{2}  

a)

16

b)

4

c)

5

d)

8

104.

Solve for s:
ss+2+s=5s+8s+2\frac{s}{s+2}+s=\frac{5s+8}{s+2}  

a)

2

b)

4

c)

6

d)

8

105.

Solve for w:
4w−2=−1w+3\frac{4}{w-2}=\frac{-1}{w+3}  

a)

2

b)

-2

c)

4

d)

-4

106.

Solve for x:
6x−1=4x−2+2x+1\frac{6}{x-1}=\frac{4}{x-2}+\frac{2}{x+1}  

a)

1

b)

2

c)

-1

d)

No Solution

107.

Simplify the following expression:
9y2−12y−1×1−2y3y−1\frac{9y^2-1}{2y-1}\times\frac{1-2y}{3y-1}

a)

−3y−1-3y-1

b)

3y+13y+1

c)

−3y+1-3y+1

d)

3y−13y-1

108.

Solve: 3x−5−20x2−25=2x+5\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}  

a)

x=−5x=-5  

b)

x=5x=5  

c)

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

d)

No Solution

109.

Solve for x:
2x+2+5x−2=6x2−4\frac{2}{x+2}+\frac{5}{x-2}=\frac{6}{x^2-4}  

a)

x = 7

b)

x = 6

c)

x = 14

d)

x = 0

110.

Solve for x:  6x+18x2+1x=3x\frac{6x+18}{x^2}+\frac{1}{x}=\frac{3}{x}  

a)

x = 9/2

b)

x = -9/2

c)

x = 3

d)

x = -3

111.

Solve for x:
5x−2+x−6x2−2x=1x\frac{5}{x-2}+\frac{x-6}{x^2-2x}=\frac{1}{x}  

a)

x = 5

b)

x = 45\frac{4}{5}

c)

x = 1

d)

x = - 4

112.

Solve for x:

xx+2+2x2+5x+6=5x+3\frac{x}{x+2}+\frac{2}{x^2+5x+6}=\frac{5}{x+3}  

a)

x=4x=4  

b)

x=−2x=-2  

c)

x={−2, 4}x=\left\{-2,\ 4\right\}  

d)

No Solution

113.

When the same number is subtracted from the denominator of 57\frac{5}{7} is added to its numerator, the resulting fraction is  13\frac{1}{3} .  Find the number.

a)

-2

b)

-4

c)

2

d)

4

114.
State the domain restrictions. 
a)
x ≠ -2
b)
x ≠ 2, 1
c)
x ≠ 2, -1
d)
x ≠ -2, 2, 1
115.

Solve the equation for x.

a)

x = 7

b)

x = 6

c)

x = 14

d)

x = 0

116.

What is the least common multiple of x2-16 and x2+4x-32?

a)

(x + 4)(x – 4)(x + 8)

b)

(x-4)2 (x+8)

c)

(x + 4)(x – 4)

d)

(x - 4)(x-4)2(x + 8)

117.
Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?
a)
48 minutes
b)
50 minutes
c)
24 minutes
d)
12 minutes
118.

Which of the following equations makes the most sense for the following situation: Jerry works twice as fast as Kenny. If Jerry works for 2 hours and is then joined by Kenny...and they work an additional 3 hours...how fast could they each do the job alone?

a)

5x+32x=1\frac{5}{x}+\frac{3}{2x}=1

b)

52x+3x=1\frac{5}{2x}+\frac{3}{x}=1

c)

x3+2x5=1\frac{x}{3}+\frac{2x}{5}=1

d)

5x+3x−2=1\frac{5}{x}+\frac{3}{x-2}=1

119.

One crew can sow a field of corn in 6 days. A different crew can do the same job in 3 days. If the slow crew works alone for 2 days and then is joined by the faster crew, how long will it take them to finish?

a)

34\frac{3}{4} of a day longer

b)

2122\frac{1}{2} more days

c)

not enough information to tell

d)

1131\frac{1}{3} days longer

120.

One computer can process payroll in 4 hours and a different computer can process it in 6 hours. If they start working at 10:00 a.m., when will they be done?

a)

11:30 a.m.

b)

1:00 p.m.

c)

12:24 p.m.

d)

12:48 p.m.

121.

Solve by cross multiplying

93x=4x+2\frac{9}{3x}=\frac{4}{x+2}  

a)

x = 3

b)

x = 4

c)

x = 6

d)

x = 1/2

e)

x = 1/3

122.

Solve by cross multiplying

x2x+7=x−5x−1\frac{x}{2x+7}=\frac{x-5}{x-1}  

a)

x = -1 x = 2

b)

x = -1, x = 7

c)

x = -1, x = 3

d)

x = -5, x = 2

e)

x = -5, x = 7

123.

Solve by cross multiplying

83x−2=2x−1\frac{8}{3x-2}=\frac{2}{x-1}  

a)

x = 1/2

b)

x = 1

c)

x = 2

d)

x = 3

e)

x = 2/3

124.

Solve by cross multiplying

−2x−1=x−8x+1\frac{-2}{x-1}=\frac{x-8}{x+1}  

a)

x = 3, x = 4

b)

x = 2, x = 5

c)

x = 1/2, x = 6

d)

x = 1, x = 3

e)

x = 2, x =4

125.

Solve the Equation by using the LCD
4x+1x+1=12x2−1+3\frac{4x+1}{x+1}=\frac{12}{x^2-1}+3  

a)

x = -1, x = 5

b)

x = -1, x = 6

c)

x = -2, x = 5

d)

x = -2, x = 6

e)

x = -3, x = 5

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