Rewrite the rational expression with the indicated denominator.
87)
5(x +1)
x(x –4) =?
x3–9x2+20x
87)
A)
5(x +1)(x –4)
x3–9x2+20x
B)
(x +1)(x –5)
x3–9x2+20x
C)
5(x +1)(x –5)
x3–9x2+20x
D)
5(x +1)(x +5)
x3–9x2+20x
Multiply or divide. Write the answer in lowest terms.
88)
2t2– 3t –9
3t2– 3t –6
·3t2+ 12t –36
t2+ 3t –18
88)
A)
(2t + 3)(t +3)
(t + 6)(3t –6)
B)
2t + 3
t + 1
C)
2t + 3
t – 1
D)
(2t + 3)(t + 6)
(t + 1)(t – 6)
Solve the problem.
89)
If the average cost per unit C(x) to produce x units of plywood is given by C(x) =1500
x + 50 , what is the
unit cost for 50 units?
89)
A)
$0.60
B)
$30.00
C)
–$20.00
D)
$15.00
Add or subtract. Write the answer in lowest terms.
90)
6a + 9b
2 –6a – 9b
2
90)
A)
9b
B)
81b
C)
0
D)
6a
Solve the problem.
91)
One printer can do a printing job in 2 hr. Another printer can do the same job in 13 hr. How long
does it take the two printers to do the job working together?
91)
A)
24
11 hr
B)
15
8 hr
C)
111
15 hr
D)
1
15 hr
Find the numerical value of the rational expression for the given value of x.
92)
6x – 7
4 x , x = 3
92)
A)
–5
4
B)
25
12
C)
11
12
D)
56
43
C
Write the rational expression in lowest terms.
93)
8– m
m – 8
93)
A)
1
B)
–m
C)
–1
D)
Already in lowest terms
C
Multiply or divide as indicated. Write the answer in lowest terms.
94)
2t2– 5t –12
3t2– 3t –6
·3t2+ 12t –36
t2+ 2t –24
94)
A)
(2t + 3)(t +4)
(t + 6)(3t –6)
B)
(2t + 3)(t + 6)
(t + 1)(t – 6)
C)
2t + 3
t + 1
D)
2t + 3
t – 1
C
22
C
Multiply. Write the answer in lowest terms.
95)
3r –9
10r2+20r
·5r +10
18 –6r
95)
A)
–3
4(3 – r)
B)
–1
4r
C)
1
4
D)
r – 3
4r(3 – r)
Simplify the complex fraction.
96)
7m7n4
5m
4m2n8
5n2
96)
A)
7m4
4n3
B)
7m5
4n3
C)
7m5
4n10
D)
7m4
4n2
Solve the formula for the specified variable.
97)
I =E
R + r for r
97)
A)
r =E – R
I
B)
r =E – IR
I
C)
r =E
I– IR
D)
r =IR
E
Multiply or divide as indicated. Write the answer in lowest terms.
98)
k2+ 11k + 30
k2+ 13k + 40
·k2+ 8k
k2+ 8k + 12
98)
A)
1
k + 2
B)
k
k2+ 13k + 40
C)
k
k + 2
D)
k2+ 8k
k + 2
23
Solve the equation.
99)
x – 5
2=x + 5
5
99)
A)
5
2
B)
{5}
C)
7
2
D)
35
3
Provide an appropriate response.
100)
In a fraction, what operation does the fraction bar represent?
100)
A)
Subtraction
B)
Addition
C)
Division
D)
Multiplication
Add or subtract. Write the answer in lowest terms.
101)
x
2–1
5
101)
A)
x – 1
7
B)
x – 1
10
C)
5x + 2
–2
D)
5x – 2
10
Find all values that make the expression undefined.
102)
x2– 36
x2– 11x + 24
102)
A)
6, –6
B)
–8, –3
C)
0
D)
8, 3
Add or subtract. Write the answer in lowest terms.
103)
8–7y
45 –9–2y
25
103)
A)
–17y + 121
225
B)
–53y + 121
225
C)
–53y – 41
225
D)
–17y – 41
225
Multiply or divide as indicated. Write the answer in lowest terms.
104)
y3– 5y
y2– 25
÷y2+ 19y + 90
y2+ 15y + 50
104)
A)
y
y + 9
B)
(y – 5)(y + 9)
y(y2– 5)
C)
(y + 5)(y – 9)
y(y2– 5)
D)
y(y2– 5)
(y – 5)(y + 9)
Write the rational expression in lowest terms.
105)
y2+ 4y – 12
y2+ 5y – 14
105)
A)
y + 6
y + 7
B)
4y – 12
5y – 14
C)
–y2+ 4y – 12
y2+ 5y – 14
D)
4y – 6
5y – 7
Solve the problem.
106)
In a certain fraction, the numerator is 3 less than the denominator. If 2 is added to both the
numerator and the denominator, the resulting fraction is equal to 1
4. What was the original fraction
(not necessarily written in lowest terms)?.
106)
A)
–1
2
B)
5
2
C)
2
–1
D)
2
5
Write the rational expression in lowest terms.
107)
tx + t +2x +2
3x +3
107)
A)
t +3
3
B)
t –2
3
C)
t +2
3
D)
t –3
2
Find the numerical value of the rational expression for the given value of x.
108)
(–7x)3
2x + 3 , x = 3
108)
A)
3087
B)
– 1029
C)
– 3087
D)
1029
Rewrite the rational expression with the indicated denominator.
109)
5
2x = ?
4x2
109)
A)
10x
4x2
B)
10
4x2
C)
5x2
4x2
D)
5
4x2
Solve the problem.
110)
Find an expression that represents the perimeter of the rectangle. Give the simplified form.
15k + 21
4
3
5k + 7
110)
A)
75k2+ 210k + 147
2(5k + 7)
B)
75k2+ 210k + 159
4(5k + 7)
C)
9
4
D)
75k2+ 210k + 159
2(5k + 7)
Multiply or divide as indicated. Write the answer in lowest terms.
111)
4(k –7)2
15(k +7) ·5(k +7)2
12(k –7)
111)
A)
20(k +7)
(k –7)
B)
(k +7)(k –7)
9
C)
(k +7)2
9
D)
5(k –7)
(k +7)
Solve the equation.
112)
x
5–x
6=8
112)
A)
240
B)
{48}
C)
{30}
D)
{40}
Find the LCD for the fractions in the list.
113)
3
n , –4
6+ n , 2
6– n
113)
A)
n + 6
B)
n(6+ n)(6– n)
C)
n2+ 36
D)
36n2
114)
3
x4 , 8
x7
114)
A)
2x4
B)
x7
C)
x4
D)
8x7
Multiply or divide as indicated. Write the answer in lowest terms.
115)
3x2– 8xy – 3y2
y2+ 2xy – 3x2·y2+ 3xy – 4x2
15x2+ 8xy + y2÷4x2– 11xy – 3y2
15x2– 2xy – y2
115)
A)
3x – y
3x + y
B)
(y + 4x)2
2x – y
C)
x – 3y
y + 3x
D)
1
Solve the equation.
116)
1
x –1+4
4x –4=2
116)
A)
{0}
B)
{2}
C)
{1}
D)
{16}
Rewrite the rational expression with the indicated denominator.
117)
–4
9m = ?
18m
117)
A)
–8
18m
B)
2
18m
C)
–4
18m
D)
9
18m
Add or subtract. Write the answer in lowest terms.
118)
1
m – n2+2
n2– m
118)
A)
2
m – n2
B)
3
m – n2
C)
–1
m – n2
D)
1
m – n2
Multiply or divide. Write the answer in lowest terms.
119)
x2+ 16x + 64
x2– 36
·x – 6
x + 8
119)
A)
x + 8
x – 6
B)
x + 8
x + 6
C)
x + 8
(x + 6)2
D)
x – 8
x + 6
Write the rational expression in lowest terms.
120)
30k3
6k
120)
A)
5k
B)
24
C)
5k2
D)
24k2
Simplify the expression, using only positive exponents in your answer.
121)
x–5+y–5
x–1+y–1
121)
A)
y5+x5
x4y5+x5y4
B)
y5+x5
x4+y4
C)
1
x + y
D)
1
x4+y4
Simplify the complex fraction.
122)
9
y
6
y +7
122)
A)
3(y +7 )
2 y
B)
54 y(y +7 )
C)
y +7
54 y
D)
2 y
3(y +7 )
Provide an appropriate response.
123)
True or false? If a is a multiple of c , then the LCD for 1
a and 1
c is ac.
123)
A)
True
B)
False
Solve the problem.
124)
A boat goes 160 mi downstream in the same time it can go 120 mi upstream. The speed of the
current is 9 mph. Find the speed of the boat in still water.
124)
A)
54 mph
B)
63 mph
C)
72 mph
D)
28 mph
Rewrite the rational expression with the indicated denominator.
125)
a
a + 5b=?
a2– 25b2
125)
A)
a
a2– 25b2
B)
5ab
a2– 25b2
C)
a2– b2
a2– 25b2
D)
a2– 5ab
a2– 25b2
Add or subtract. Write the answer in lowest terms.
126)
7x – z
7x2–49xz +4xz –28z2–x + z
x2–49z2
126)
A)
14x2+ 37xz – 3z2
(x –7z)(x +7z)(7x +4z)
B)
37xz –11z2
(x –7z)2(7x +4z)
C)
37xz +11z2
(x –7z)(x +7z)(7x +4z)
D)
37xz –11z2
(x –7z)(x +7z)(7x +4z)
127)
5m
m – 2 +
–10
m – 2
127)
A)
5
B)
5
m – 2
C)
0
D)
5(m + 2)
m – 2
128)
5x
x +6+2
x –6
128)
A)
5x +2
(x +6)(x –6)
B)
5x2– 28x +12
x2–36
C)
5x2– 28x +12
x2–12x +36
D)
5x2– 28x +12
x2+12x +36
Multiply or divide as indicated. Write the answer in lowest terms.
129)
x2+10x +24
x2+6x
·6x
x2+8x +16
÷x +6
x +4
129)
A)
x +4
x +6
B)
1
x +6
C)
x
x +6
D)
6
x +6
Simplify the complex fraction.
130)
1
k +6
5
k2–36
130)
A)
5
k –6
B)
k –6
5
C)
k +6
5
D)
k –6
Add or subtract. Write the answer in lowest terms.
131)
5
7x –7–1
7–7 x
131)
A)
–4
7x –7
B)
–6
7x –7
C)
4
7x –7
D)
6
7x –7
Multiply or divide as indicated. Write the answer in lowest terms.
132)
x2+6x +8
x +4÷x2–4
4x –8
132)
A)
4x –8
x –2
B)
1
4
C)
(x +2)2
4
D)
4
Find the numerical value of the rational expression for the given value of x.
133)
5– 5 x
3 x2– 2 x + 5 , x = – 3
133)
A)
–5
13
B)
–5
19
C)
10
13
D)
10
19
Solve the problem.
134)
One maid can clean the house in 7 hr. Another maid can do the job in 8 hr. How long will it take
them to do the job working together?
134)
A)
1
56 hr
B)
56 hr
C)
311
15 hr
D)
1
15 hr
Solve the equation.
135)
2
y + 2 –5
y – 2 =7
y2– 4
135)
A)
{7}
B)
{21}
C)
{–7}
D)
Find the numerical value of the rational expression for the given value of r.
136)
r2– r +5
r2+ 10r + 21 , r = – 3
136)
A)
5
37
B)
5
C)
0
D)
Undefined
Multiply or divide as indicated. Write the answer in lowest terms.
137)
2a –2b –a2+b2
25a2–10ab +b2·25a2–b2
5a2– 4ab –b2
137)
A)
5a – b
2– a – b
B)
2+ a + b
5a – b
C)
2– a – b
5a – b
D)
2– a – b
Simplify the complex fraction.
138)
4
3r – 1 –4
4
3r – 1 +4
138)
A)
2 +3 r
3 r
B)
2 – r
r
C)
3 r
2 –3 r
D)
2 –3 r
3 r
Solve the problem.
139)
A plane flies 440 mi with the wind and 350 mi against the wind in the same length of time. If the
speed of the wind is 27 mph, what is the speed of the plane in still air?
139)
A)
227 mph
B)
242 mph
C)
262 mph
D)
237 mph
Find the LCD for the fractions in the list.
140)
3
x2– 4x – 5 , 3
x2– 2x – 15
140)
A)
(x – 1)(x + 5)(x + 3)
B)
(x + 1)(x – 5)
C)
(x + 1)(x – 5)(x + 3)
D)
(x – 5)(x + 3)
141)
3
10 , 7
6
141)
A)
30
B)
6
C)
15
D)
10
Identify as an equation or an expression.
142)
–5 ( 2 – x) +8x +7
5
142)
A)
Expression
B)
Equation
Simplify the complex fraction.
143)
5
9
5
16
143)
A)
16
9
B)
25
144
C)
9
16
D)
2
5
Provide an appropriate response.
144)
Which of the following fractions is equivalent to
1
7+1
14
1
3+1
12
?
144)
A)
–18
35
B)
18
35
C)
–35
18
D)
12
Find all values that make the expression undefined.
145)
8
r+ 7
145)
A)
0
B)
Never undefined
C)
7
D)
–7
Find all values for which at least one denominator is equal to 0. Write answers using the symbol . Do not solve.
146)
5
x – 8 –14
x + 1 = 0
146)
A)
x 8, –1, 5, 14
B)
x 8, –1
C)
x –8, 1
D)
x –8, 1, –5, –14
B
Find the numerical value of the rational expression for the given value of r.
147)
6r + 7
2 r2+ 3 r + 7 , r = – 4
147)
A)
–31
27
B)
–17
27
C)
–17
37
D)
31
27
B
Add or subtract. Write the answer in lowest terms.
148)
7
11x+3
11x
148)
A)
11x
10
B)
10
11x
C)
10
22x
D)
1
B
D
Multiply or divide as indicated. Write the answer in lowest terms.
149)
2r –6
10r2+20r
·5r +10
12 –4r
149)
A)
–2
4(3 – r)
B)
1
4
C)
–1
4r
D)
r – 3
4r(3 – r)
Add or subtract. Write the answer in lowest terms.
150)
b
b2– 25
+5
b + 5 –6
b
150)
A)
25(b – 6)
(b + 5)(b – 5)
B)
–25(b – 6)
b(b + 5)(b – 5)
C)
6b2– 25b + 150
b(b + 5)(b – 5)
D)
25(b + 6)
b(b + 5)(b – 5)
Find all values for which at least one denominator is equal to 0. Write answers using the symbol . Do not solve.
151)
6x + 1
x + 9 =14 x – 19
14 x – 15
151)
A)
x 0, –9, 15
14 , –1
6, 19
14
B)
x –1
6, 19
14
C)
x –9, 15
14
D)
x –9, 15
14 , –1
6, 19
14
Solve the problem.
152)
The area of the rectangle is represented by y2+ 6y + 8. What is the width?
y + 2
152)
A)
y + 4
B)
y – 6
C)
y + 6
D)
y – 4
Provide an appropriate response.
153)
True or false? If x d and x e are denominators of two fractions and d>e, then x d is the LCD.
153)
A)
True
B)
False
Simplify the complex fraction.
154)
–3
2
–3
8
154)
A)
1
4
B)
4
C)
9
16
D)
–3
5
Solve the equation.
155)
x + 5
6=x + 6
7
155)
A)
11
42
B)
{1}
C)
1
42
D)
11
13
Solve.
156)
–2 x
2x +2=2 x
4x +4+2x –4
x +1
156)
A)
1
14
B)
8
7
C)
–8
7
D)
{16}
Find the LCD for the fractions in the list.
157)
1
63x2 , 6
7x3
157)
A)
7x3
B)
63x2
C)
63x5
D)
63x3
D
Write the rational expression in lowest terms.
158)
5+ t
t – 5
158)
A)
–t
B)
–1
C)
1
D)
Already in lowest terms
D
Multiply or divide as indicated. Write the answer in lowest terms.
159)
y2– 16
3y – 12 ÷y + 4
y + 7
159)
A)
(y + 7)(y + 4)
3(y + 4)
B)
1
3
C)
y + 7
3
D)
y + 7
C
B
Find the LCD for the fractions in the list.
160)
9
t , 7
t – 7
160)
A)
t
B)
63
C)
t – 7
D)
t(t – 7)
Solve the problem.
161)
Find an expression that represents the area of the rectangle. Give the simplified form.
10p – 6
5
3
5p – 3
161)
A)
2
5
B)
6
5
C)
3
5
D)
5
6
Find the LCD for the fractions in the list.
162)
1
r2+ 16r + 64 , 6
r2+ 8r
162)
A)
r(r + 8)2
B)
r(r + 8)
C)
(r + 8)2
D)
r(r + 1)(r + 8)
Find the least common denominator for the fractions in the list.
163)
–1
30x5, 1
54x4, –6
45x2
163)
A)
135x20
B)
54x2
C)
270x5
D)
90x5