Deck 7: Rational Expressions and Equations

Question 1

Simplify.
$$\frac { 5 x - 25 } { x ^ { 2 } - 5 x }$$

A) 5
B) $\frac { 5 } { x }$
C) $5 x$
D) $\frac { x } { 5 }$

Answer 1

B

Question 2

Simplify.
$$\frac { y ^ { 2 } - 2 y - 8 } { y ^ { 2 } - 4 y - 12 }$$

A) $- \frac { y ^ { 2 } - 2 y - 8 } { y ^ { 2 } - 4 y - 12 }$
B) $\frac { - 2 y - 8 } { - 4 y - 12 }$
C) $\frac { - 2 y - 2 } { - 4 y - 3 }$
D) $\frac { y - 4 } { y - 6 }$

Answer 2

D

Question 3

Simplify.
$$\frac { x + 5 y } { 3 x + 15 y }$$

A) $\frac { 1 } { 3 }$
B) 3
C) 1
D) $\frac { 1 } { 3 ( x - 5 y ) }$

Answer 3

A

Question 4

Simplify.
$$\frac { 3 x + 15 } { 2 x ^ { 2 } + 17 x + 35 }$$

A) $\frac { 3 x + 15 } { 2 x ^ { 2 } + 17 x + 35 }$
B) $\frac { 3 x } { 2 x + 7 }$
C) $\frac { 3 } { 2 x + 7 }$
D) $\frac { 3 x + 2 } { 2 x + 17 }$

Question 5

Simplify.
$$\frac { 6 - 2 x } { 7 x ^ { 2 } - 21 x }$$

A) $\frac { 2 ( 3 - x ) } { 7 x ( x - 3 ) }$
B) $- \frac { 2 } { 7 x }$
C) $\frac { 2 } { 7 x }$
D) $- \frac { 2 } { 7 }$

Question 6

Simplify.
$$\frac { 1 - 9 x ^ { 2 } } { 9 x ^ { 2 } + 6 x + 1 }$$

A) $1 - 3 x$
B) $\frac { 3 x + 1 } { 1 - 3 x }$
C) $- 1$
D) $\frac { 1 - 3 x } { 3 x + 1 }$

Question 7

Perform the operation indicated.
$\frac { 2 x - 2 } { x } \cdot \frac { 7 x ^ { 2 } } { 3 x - 3 }$

A) $\frac { 6 x ^ { 2 } + 12 x + 6 } { 7 x ^ { 3 } }$
B) $\frac { 14 x } { 3 }$
C) $\frac { 3 } { 14 x }$
D) $\frac { 14 x ^ { 3 } - 14 x ^ { 2 } } { 3 x ^ { 2 } - 3 x }$

Question 8

Simplify.
$$\frac { 8 x ^ { 2 } + 24 x ^ { 3 } } { 5 x + 15 x ^ { 2 } }$$

A) $\frac { 8 + 24 x ^ { 3 } } { 5 x + 15 }$
B) $\frac { 8 } { 5 }$
C) $\frac { 8 x ^ { 2 } + 24 x ^ { 3 } } { 5 x + 15 x ^ { 2 } }$
D) $\frac { 8 x } { 5 }$

Question 9

Simplify.
$$\frac { 24 - 6 a b } { a b ^ { 2 } - 4 b }$$

A) $- 6 b$
B) $\frac { 6 ( 4 - a b ) } { b ( a b - 4 ) }$
C) $- \frac { 6 } { b }$
D) $\frac { 6 } { b }$

Question 10

Simplify.
$$\frac { 3 a - 9 b } { a - 3 b }$$

A) 1
B) 3
C) $\frac { 3 } { a - 5 b }$
D) $3 ( a - 5 b )$

Question 11

Simplify.
$$\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }$$

A) $\frac { 2 x + 3 } { 3 x + 16 }$
B) $\frac { 2 x + 2 } { 6 x ^ { 2 } + 16 x + 10 }$
C) $\frac { 2 x } { 3 x + 5 }$
D) $\frac { 1 } { 3 x + 5 }$

Question 12

Perform the operation indicated.
$\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }$

A) $\frac { 5 x } { 4 }$
B) $\frac { 5 x } { 12 }$
C) $\frac { x } { 4 }$
D) $\frac { 5 } { 4 }$

Question 13

Simplify.
$$\frac { 1 - x ^ { 2 } } { 2 x ^ { 2 } + 3 x - 5 }$$

A) $\frac { - x - 1 } { 2 x - 5 }$
B) $\frac { x + 1 } { 2 x + 5 }$
C) $\frac { - x - 1 } { 2 x + 5 }$
D) $\frac { ( 1 + x ) ( 1 - x ) } { ( 2 x + 5 ) ( x - 1 ) }$

Question 14

Simplify.
$$\frac { 4 x ^ { 2 } - 13 x + 9 } { x - 1 }$$

A) $\frac { 1 } { x - 1 }$
B) $4 x ^ { 2 } - 22$
C) $\frac { 4 x ^ { 2 } - 13 x + 9 } { x - 1 }$
D) $4 x - 9$

Question 15

Simplify.
$\frac { 7 a ^ { 2 } b ( a + 4 b ) } { 28 a b ^ { 2 } }$

A) $\frac { a ( a + 4 b ) } { 4 b }$
B) $\frac { a } { 4 b }$
C) $\frac { a b ( a + 4 b ) } { 4 }$
D) $\frac { ( a + 4 b ) } { 4 a b }$

Question 16

Simplify.
$$\frac { 2 x ^ { 2 } - 3 x + - 5 } { 3 x ^ { 2 } + 2 x + - 1 }$$

A) $\frac { ( 2 x - 5 ) ( x - 1 ) } { ( 3 x - 1 ) ( x + 1 ) }$
B) $\frac { 2 x + 5 } { 3 x + 1 }$
C) $\frac { 2 x - 5 } { 3 x + 1 }$
D) $\frac { 2 x - 5 } { 3 x - 1 }$

Question 17

Simplify.
$$\frac { ( 7 x - 5 ) ^ { 2 } } { 7 x ^ { 2 } - 61 x + 40 }$$

A) $7 x - 5$
B) $\frac { ( 7 x - 5 ) ^ { 2 } } { ( x - 8 ) ( 7 x + 5 ) }$
C) $\frac { 1 } { x - 8 }$
D) $\frac { 7 x - 5 } { x - 8 }$

Question 18

Simplify.
$$\frac { y ^ { 2 } + 9 y + 20 } { y ^ { 2 } + 10 y + 24 }$$

A) $\frac { 9 y + 20 } { 10 y + 24 }$
B) $- \frac { y ^ { 2 } + 9 y + 20 } { y ^ { 2 } + 10 y + 24 }$
C) $\frac { y + 5 } { y + 6 }$
D) $\frac { 9 y + 5 } { 10 y + 6 }$

Question 19

Simplify.
$$\frac { x ^ { 3 } + 10 x ^ { 2 } + 21 x } { x ^ { 2 } + 12 x + 35 }$$

A) $\frac { x + 3 } { x + 5 }$
B) $\frac { x ^ { 3 } + 10 x ^ { 2 } + 21 x } { x ^ { 2 } + 12 x + 35 }$
C) $\frac { x ( x + 3 ) } { x + 5 }$
D) $\frac { x + 3 } { x ( x + 5 ) }$

Question 20

Simplify.
$\frac { 3 x + 6 } { 2 x + 4 }$

A) $- 1$
B) $\frac { 3 } { 2 }$
C) $\frac { 2 } { 3 }$
D) 1

Question 21

Perform the operation indicated.
$$\frac { x ^ { 2 } + 14 x + 45 } { x ^ { 2 } + 15 x + 54 } \div \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 4 x - 12 }$$

A) $\frac { x } { x ^ { 2 } + 15 x + 54 }$
B) $\frac { x - 2 } { x }$
C) $\frac { x - 2 } { x ^ { 2 } + 6 x }$
D) $x - 2$

Question 22

Perform the operation indicated.
$$\frac { 14 x ^ { 2 } - 23 x y - 30 y ^ { 2 } } { 49 x ^ { 2 } + 63 x y + 18 y ^ { 2 } } + \frac { 10 x ^ { 2 } - 37 x y + 30 y ^ { 2 } } { 20 x ^ { 2 } - 49 x y + 30 y ^ { 2 } }$$

A) $\frac { ( 7 x - 3 y ) } { ( 4 x + 5 y ) }$
B) $\frac { ( 2 x + 5 y ) ^ { 2 } } { ( 4 x + 5 y ) ( 7 x - 3 y ) }$
C) $\frac { 4 x - 5 y } { 7 x + 3 y }$
D) $\frac { ( 2 x - 5 y ) ^ { 2 } } { ( 4 x - 5 y ) ( 7 x + 3 y ) }$

Question 23

Perform the operation indicated.
$$\frac { x ^ { 2 } + 11 x + 18 } { x ^ { 2 } + 18 x + 81 } \div \frac { x ^ { 2 } + 2 x } { x ^ { 2 } + 14 x + 45 }$$

A) $\frac { x + 5 } { x }$
B) $x + 5$
C) $\frac { x } { x ^ { 2 } + 18 x + 81 }$
D) $\frac { x + 5 } { x ^ { 2 } + 9 x }$

Question 24

Perform the operation indicated. Simplify.
$$\frac { 4 } { 11 + x } + \frac { x + 2 } { 11 + x }$$

A) $\frac { 6 } { 11 }$
B) $\frac { x + 6 } { 22 + x }$
C) $\frac { 6 } { 22 }$
D) $\frac { x + 6 } { 11 + x }$

Question 25

Perform the operation indicated.
$$\frac { 15 r ^ { 2 } - 14 r t - 8 t ^ { 2 } } { 10 r ^ { 2 } - 21 r t - 10 t ^ { 2 } } \cdot \frac { 30 r ^ { 2 } - 11 r t - 28 t ^ { 2 } } { 15 r ^ { 2 } - 8 r t - 16 t ^ { 2 } }$$

A) $\frac { 6 r - 7 t } { 2 r - 5 t }$
B) $\frac { ( 3 r + 4 t ) ^ { 2 } } { ( 6 r + 7 t ) ( 2 r + 5 t ) }$
C) $\frac { ( 3 r - 4 t ) ^ { 2 } } { ( 6 r - 7 t ) ( 2 r - 5 t ) }$
D) $\frac { ( 2 r + 5 t ) } { ( 6 r + 7 t ) }$

Question 26

Perform the operation indicated.
$$\frac { 3 x - 3 } { x } + \frac { 7 x - 7 } { 4 x ^ { 2 } }$$

A) $\frac { 7 } { 12 x }$
B) $\frac { 12 x ^ { 3 } - 12 x ^ { 2 } } { 7 x ^ { 2 } - 7 x }$
C) $\frac { 21 x ^ { 2 } + 42 x + 21 } { 4 x ^ { 3 } }$
D) $\frac { 12 x } { 7 }$

Question 27

Perform the operation indicated. Simplify.
5x + 6 x - 1 2x - 5 + 2x - 5

A)4x + 5
B)6x + 5
C)4x + 7
D)6x + 7

Question 28

Perform the operation indicated. Simplify.
$\frac { 9 x ^ { 2 } } { x - 1 } - \frac { 9 x } { x - 1 }$

A) $\frac { 9 x } { x - 1 }$
B) 9
C) $\frac { 9 x ( x + 1 ) } { x - 1 }$
D) $9 \mathrm { x }$

Question 29

Perform the operation indicated. Simplify.
$$\frac { x } { x + 4 } + \frac { 6 x + 5 } { 4 + x }$$

A) $\frac { 7 x + 5 } { x + 4 }$
B) $\frac { x + 5 } { x + 4 }$
C) $\frac { 5 x + 5 } { x + 4 }$
D) $\frac { 7 x } { x + 4 }$

Question 30

Perform the operation indicated.
$$\frac { x ^ { 2 } - 13 x + 40 } { x ^ { 2 } - 13 x + 42 } \cdot \frac { x ^ { 2 } - 19 x + 84 } { x ^ { 2 } - 19 x + 88 }$$

A) $\frac { \left( x ^ { 2 } - 13 x + 40 \right) \left( x ^ { 2 } - 19 x + 84 \right) } { \left( x ^ { 2 } - 13 x + 42 \right) \left( x ^ { 2 } - 19 x + 88 \right) }$
B) $\frac { ( x - 5 ) ( x - 12 ) } { ( x - 6 ) ( x - 11 ) }$
C) $\frac { ( x - 5 ) } { ( x - 11 ) }$
D) $\frac { ( x + 5 ) ( x + 12 ) } { ( x + 6 ) ( x + 11 ) }$

Question 31

Perform the operation indicated.
$$\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } + 10 x + 24 } \cdot \frac { x ^ { 2 } + 6 x } { x ^ { 2 } + 8 x + 15 }$$

A) $\frac { x } { x ^ { 2 } + 10 x + 24 }$
B) $\frac { x ^ { 2 } + 6 x } { x + 5 }$
C) $\frac { 1 } { x + 5 }$
D) $\frac { x } { x + 5 }$

Question 32

Perform the operation indicated. Simplify.
$$\frac { 5 x } { x - 4 } - \frac { 20 } { x - 4 }$$

A) $\frac { 5 ( x + 4 ) } { x - 4 }$
B) $\frac { 5 } { x - 4 }$
C) 5
D) 1

Question 33

Perform the operation indicated. Simplify.
$$\frac { 7 x - 12 } { x - 1 } - \frac { 2 x - 8 } { x - 1 }$$

A) $\frac { 5 x - 4 } { x - 1 }$
B) $\frac { 5 x + 20 } { x - 1 }$
C) $\frac { 5 x - 20 } { x - 1 }$
D) $\frac { 5 x + 4 } { x - 1 }$

Question 34

Perform the operation indicated.
$$\frac { x ^ { 2 } + 13 x + 42 } { x ^ { 2 } + 9 x + 14 } \cdot \frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } + 9 x + 18 }$$

A) $\frac { x + 6 } { x + 2 }$
B) $\frac { x + 2 } { x + 6 }$
C) $\frac { 1 } { x + 3 }$
D) 1

Question 35

Perform the operation indicated.
$$\frac { x ^ { 2 } - 12 x + 11 } { 11 - x } \div ( x + 1 )$$

A) $- \frac { x + 1 } { x - 1 }$
B) $- \frac { x - 1 } { x + 1 }$
C) $- 1$
D) $- ( x - 1 ) ( x + 1 )$

Question 36

Perform the operation indicated.
$$\frac { x ^ { 2 } + 9 x + 20 } { x ^ { 2 } + 11 x + 28 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } - 2 x - 35 }$$

A) $\frac { x ^ { 2 } + 7 x } { x - 7 }$
B) $\frac { x } { x - 7 }$
C) $\frac { x } { x ^ { 2 } + 11 x + 28 }$
D) $\frac { 1 } { x - 7 }$

Question 37

Perform the operation indicated.
$\frac { 27 x - 27 } { 2 } \div \frac { 9 x - 9 } { 10 }$

A) $\frac { 243 ( x - 1 ) ^ { 2 } } { 20 }$
B) $\frac { 1 } { 15 }$
C) $\frac { 5 ( 27 x - 27 ) } { 9 x - 9 }$
D) 15

Question 38

Perform the operation indicated. Simplify.
$$\frac { 2 x } { x - 5 } - \frac { x + 2 } { x - 5 }$$

A) $\frac { x + 2 } { x - 5 }$
B) $\frac { 3 x + 2 } { x - 5 }$
C) $\frac { 3 x - 2 } { x - 5 }$
D) $\frac { x - 2 } { x - 5 }$

Question 39

Perform the operation indicated.
$$\frac { x ^ { 2 } - 20 x + 100 } { 7 x - 70 } \div \frac { 2 x - 20 } { 14 }$$

A) 14
B) $\frac { ( x - 10 ) ^ { 2 } } { 49 }$
C) $\frac { x ^ { 2 } - 20 x + 100 } { ( x - 10 ) ^ { 2 } }$
D) 1

Question 40

Perform the operation indicated.
$$\frac { ( x - 9 ) ^ { 2 } } { 3 } \div \frac { 3 x - 27 } { 9 }$$

A) $\frac { 3 ( x - 9 ) ^ { 2 } } { 3 x - 27 }$
B) $x - 9$
C) $\frac { 1 } { x - 9 }$
D) $\frac { ( x - 9 ) ^ { 3 } } { 9 }$

Question 41

Find the LCD. Do not combine fractions.
$$\frac { 2 } { 4 x - 32 } , \frac { 6 } { x ^ { 2 } - 8 x }$$

A) $4 x - 8$
B) $4 x ^ { 2 } - 32$
C) $4 x ^ { 2 } - 8$
D) $4 x ( x - 8 )$

Question 42

Perform the operation indicated. Simplify.
$$\frac { 9 } { \mathrm {~cd} } + \frac { 5 } { \mathrm { c } }$$

A) $\frac { 9 \mathrm {~d} + 5 } { \mathrm {~cd} }$
B) $\frac { 9 + 5 d } { c d }$
C) $\frac { 9 + 5 c } { c d }$
D) $\frac { 14 } { c d }$

Question 43

Find the LCD. Do not combine fractions.
$$\frac { 3 } { x ^ { 2 } - 4 x - 5 } , \frac { 5 } { 3 x - 15 }$$

A) $3 ( x - 1 ) ( x + 5 )$
B) $3 ( x - 1 ) ( x - 5 )$
C) $3 ( x + 1 ) ( x - 5 )$
D) $3 ( x + 1 ) ( x + 5 )$

Question 44

Find the LCD. Do not combine fractions.
$$\frac { 1 } { x ^ { 2 } + 8 x + 16 } , \frac { 1 } { x ^ { 2 } + 4 x }$$

A) $( x + 4 ) ^ { 2 }$
B) $x ( x + 1 ) ( x + 4 )$
C) $x ( x + 4 )$
D) $x ( x + 4 ) ^ { 2 }$

Question 45

Perform the operation indicated. Simplify.
$$\frac { x ^ { 2 } - 9 x } { x - 6 } + \frac { 18 } { x - 6 }$$

A) $x + 3$
B) $\frac { x ^ { 2 } - 9 x + 18 } { x - 6 }$
C) $x - 6$
D) $x - 3$

Question 46

Find the LCD. Do not combine fractions.
$$\frac { 2 } { 3 a ^ { 2 } } , \frac { 5 } { a ^ { 3 } }$$

A) $3 a ^ { 2 }$
B) $10 a ^ { 3 }$
C) $a ^ { 3 }$
D) $3 a ^ { 3 }$

Question 47

Perform the operation indicated. Simplify.
$$\frac { x } { 2 x - 5 } - \frac { 5 } { 12 x - 30 }$$

A) $\frac { 12 x - 60 } { 6 ( 2 x - 5 ) }$
B) $\frac { x - 5 } { 6 ( 2 x - 5 ) }$
C) $\frac { 6 x - 5 } { 6 ( 2 x - 5 ) }$
D) $\frac { 6 x - 5 } { 2 x - 5 }$

Question 48

Find the LCD. Do not combine fractions.
$\frac { 8 } { 10 x y ^ { 3 } } , \frac { 2 } { 8 x ^ { 4 } y ^ { 2 } }$

A) $40 \mathrm { x } ^ { 4 } \mathrm { y } ^ { 3 }$
B) $40 x y$
C) $40 x ^ { 4 } y ^ { 2 }$
D) $40 \mathrm { xy } ^ { 3 }$

Question 49

Perform the operation indicated. Simplify.
$$\frac { 3 } { y ^ { 2 } - 3 y + 2 } + \frac { 5 } { y - 1 }$$

A) $\frac { 5 y + 7 } { ( y + 2 ) ( y - 1 ) }$
B) $\frac { 8 } { ( y - 2 ) ( y - 1 ) }$
C) $\frac { y - 7 } { ( y - 2 ) ( y - 1 ) }$
D) $\frac { 5 y - 7 } { ( y - 2 ) ( y - 1 ) }$

Question 50

Perform the operation indicated. Simplify.
$$\frac { 13 } { x - 5 } + \frac { x } { x ^ { 2 } - 25 }$$

A) $\frac { 14 x + 65 } { ( x + 5 ) ( x - 5 ) }$
B) $\frac { 14 x - 65 } { ( x + 5 ) ( x - 5 ) }$
C) $\frac { 13 x + 65 } { ( x + 5 ) ( x - 5 ) }$
D) $\frac { 13 x } { ( x + 5 ) ( x - 5 ) }$

Question 51

Find the LCD. Do not combine fractions.
$$\frac { 8 } { 12 x ^ { 2 } y ^ { 5 } } , \frac { 8 } { 16 x ^ { 3 } y ^ { 3 } }$$

A) $48 x ^ { 3 } y ^ { 3 }$
B) $48 x y$
C) $48 x ^ { 2 } y ^ { 5 }$
D) $48 x ^ { 3 } y ^ { 5 }$

Question 52

Find the LCD. Do not combine fractions.
$$\frac { 12 } { x + 9 } , \frac { 5 } { x ^ { 2 } - 81 }$$

A) $x ^ { 2 } - 81$
B) $x + 9$
C) $( x + 9 ) ( x - 9 ) ^ { 2 }$
D) $( x + 9 ) \left( x ^ { 2 } - 81 \right)$

Question 53

Perform the operation indicated. Simplify.
$$\frac { 6 } { x + 5 } - \frac { 2 } { x - 5 }$$

A) $\frac { 4 x - 20 } { ( x + 5 ) ( x - 5 ) }$
B) $\frac { 4 } { ( x + 5 ) ( x - 5 ) }$
C) $\frac { 4 x + 40 } { ( x + 5 ) ( x - 5 ) }$
D) $\frac { 4 x - 40 } { ( x + 5 ) ( x - 5 ) }$

Question 54

Find the LCD. Do not combine fractions.
$$\frac { 3 } { x ^ { 2 } - 49 } , \frac { 11 } { x - 7 }$$

A) $x - 7$
B) $x ^ { 2 } - 49$
C) $( x - 7 ) \left( x ^ { 2 } - 49 \right)$
D) $( x - 7 ) ^ { 3 }$

Question 55

Find the LCD. Do not combine fractions.
$$\frac { 9 } { 2 x + 6 } , \frac { 11 } { 5 x + 15 }$$

A) $5 ( x + 3 )$
B) $2 ( x + 3 )$
C) $( x + 3 )$
D) $10 ( x + 3 )$

Question 56

Find the LCD. Do not combine fractions.
$$\frac { 9 } { x } , \frac { 4 } { x + 1 }$$

A) $x$
B) 36
C) $x + 1$
D) $x ( x + 1 )$

Question 57

Find the LCD. Do not combine fractions.
$\frac { 4 } { 3 a b } , \frac { 5 } { a ^ { 2 } b ^ { 2 } }$

A) $3 a ^ { 2 } b ^ { 2 }$
B) $20 a ^ { 2 } b ^ { 2 }$
C) $a ^ { 2 } b ^ { 2 }$
D) $3 a b$

Question 58

Find the LCD. Do not combine fractions.
$\frac { 5 } { x ^ { 2 } - 9 x + 20 } , \frac { 9 } { x ^ { 2 } - 8 x + 16 }$

A) $( x + 5 ) ( x + 4 ) ( x - 4 )$
B) $( x - 4 ) ( x - 4 )$
C) $( x - 5 ) ( x - 4 ) ( x - 4 )$
D) $( x - 5 ) ( x - 4 )$

Question 59

Find the LCD. Do not combine fractions.
$$\frac { 4 } { x ^ { 2 } + 6 x } , \frac { 9 } { x ^ { 2 } + 3 x - 18 }$$

A) $x ( x + 9 ) ^ { 2 }$
B) $x ( x + 6 ) ( x - 3 )$
C) $x ( x + 9 ) ( x - 3 )$
D) $( x + 9 ) ^ { 2 }$

Question 60

Find the LCD. Do not combine fractions.
$$\frac { 18 x + 3 } { 15 x - 8 } , \frac { 5 x } { 15 x + 8 }$$

A) $( 15 x - 8 ) ( 15 x + 8 )$
B) $( 15 x - 8 )$ or $( 15 x + 8 )$
C) $5 x ( 18 x + 3 ) ( 15 x - 8 ) ( 15 x + 8 )$
D) $5 x ( 18 x + 3 )$

Question 61

Perform the operation indicated. Simplify.
$$\frac { 2 } { 3 a b } + \frac { 2 } { 15 b c }$$

A) $\frac { 2 c + 10 a } { 15 a b c }$
B) $\frac { 12 } { 15 a b c }$
C) $\frac { 10 c + 2 a } { 15 a b c }$
D) $\frac { 2 c + 2 a } { 15 a b c }$

Question 62

Perform the operation indicated. Simplify.
$\frac { \frac { 5 } { a } + \frac { 2 } { b } } { \frac { 1 } { x } - \frac { 1 } { y } }$

A) $\frac { x y ( 5 a + 2 b ) } { a b ( x - y ) }$
B) $\frac { a b ( 2 a + 5 b ) } { x y ( y - x ) }$
C) $\frac { x y ( 2 a + 5 b ) } { a b ( y - x ) }$
D) $\frac { 2 a + 5 b } { y - x }$

Question 63

Perform the operation indicated. Simplify.
$$\frac { 8 } { x - 6 } + \frac { 2 } { x }$$

A) $\frac { 12 x - 10 } { x ( x - 6 ) }$
B) $\frac { 12 x - 10 } { x ( 6 - x ) }$
C) $\frac { 10 x - 12 } { x ( 6 - x ) }$
D) $\frac { 10 x - 12 } { x ( x - 6 ) }$

Question 64

Perform the operation indicated. Simplify.
$$\frac { 6 x } { x + 9 } + \frac { 8 x - 3 } { x + 9 } - \frac { 3 x } { x + 9 }$$

A) $\frac { 11 x - 3 } { 3 x + 27 }$
B) $\frac { 17 x + 3 } { x - 9 }$
C) $\frac { 11 x - 3 } { x + 9 }$
D) $\frac { 17 x - 3 } { x + 9 }$

Question 65

Perform the operation indicated. Simplify.
$\frac { \frac { 5 } { x } } { \frac { 7 } { x } - \frac { 1 } { x ^ { 2 } } }$

A) $\frac { 5 x } { 7 x + 1 }$
B) $\frac { 5 x } { 7 x - 1 }$
C) $\frac { 7 x - 1 } { 5 x }$
D) $\frac { 5 x ^ { 2 } } { 7 x ^ { 2 } - 1 }$

Question 66

Perform the operation indicated. Simplify.
$$\frac { 6 - x } { x - 3 } - \frac { 2 x + 1 } { 3 - x }$$

A) $- \frac { x + 7 } { x - 3 }$
B) $\frac { x + 7 } { x - 3 }$
$C ) - \frac { x + 5 } { x - 3 }$
D) $\frac { x + 5 } { x - 3 }$

Question 67

Perform the operation indicated. Simplify.
$$\frac { 6 } { 4 x - 11 } - \frac { 19 } { 11 - 4 x }$$

A) $=- \frac { 13 } { 4 x - 11 }$
B) $\frac { 13 } { 4 x - 11 }$
C) $- \frac { 25 } { 4 x - 11 }$
D) $\frac { 25 } { 4 x - 11 }$

Question 68

Perform the operation indicated. Simplify.
$$\frac { 4 } { x ^ { 2 } - 3 x + 2 } + \frac { 5 } { x ^ { 2 } - 1 }$$

A) $\frac { 9 x - 6 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$
B) $\frac { 40 x - 6 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$
C) $\frac { 9 x - 6 } { ( x - 1 ) ( x - 2 ) }$
D) $\frac { 6 x - 9 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$

Question 69

Perform the operation indicated. Simplify.
$\frac { 5 } { 7 x } + \frac { 3 } { 8 x }$

A) $\frac { 61 } { 56 x }$
B) $\frac { 8 } { 15 x }$
C) $\frac { 59 } { 56 x }$
D) $\frac { 61 } { 56 x ^ { 2 } }$

Question 70

Perform the operation indicated. Simplify.
$$\frac { x - 5 } { x ^ { 2 } - 4 x + 3 } + \frac { 2 x + 1 } { x ^ { 2 } - 7 x + 6 }$$

A) $\frac { 3 x - 4 } { 2 x ^ { 2 } - 11 x + 9 }$
B) $\frac { 3 x ^ { 2 } - 16 x + 27 } { ( x + 1 ) ( x + 3 ) ( x + 6 ) }$
C) $3 x - 4$
D) $\frac { 3 x ^ { 2 } - 16 x + 27 } { ( x - 1 ) ( x - 3 ) ( x - 6 ) }$

Question 71

Perform the operation indicated. Simplify.
$$\frac { x - 2 } { x ^ { 2 } + 6 x + 5 } + \frac { 2 x + 5 } { x ^ { 2 } + 4 x + 3 }$$

A) $\frac { 3 x ^ { 2 } + 16 x + 19 } { ( x - 1 ) ( x - 5 ) ( x - 3 ) }$
B) $3 x + 3$
C) $\frac { 3 x ^ { 2 } + 16 x + 19 } { ( x + 1 ) ( x + 5 ) ( x + 3 ) }$
D) $\frac { 3 x + 3 } { 2 x ^ { 2 } + 10 x + 8 }$

Question 72

Perform the operation indicated. Simplify.
$$\frac { x } { x ^ { 2 } - 16 } - \frac { 4 } { 16 - x ^ { 2 } }$$

A) $\frac { 1 } { x - 4 }$
B) $- \frac { 1 } { x - 4 }$
C) $\frac { 1 } { x + 4 }$
D) $- \frac { 1 } { x + 4 }$

Question 73

Perform the operation indicated. Simplify.
$$\frac { 4 y } { x ^ { 2 } - y ^ { 2 } } + \frac { 4 x } { y ^ { 2 } - x ^ { 2 } }$$

A) $\frac { 4 } { x - y }$
B) $\frac { y - x } { x ^ { 2 } - y ^ { 2 } }$
C) $- \frac { 4 } { x + y }$
D) $\frac { 4 } { x + y }$

Question 74

Perform the operation indicated. Simplify.
$$\frac { x } { x ^ { 2 } - 16 } - \frac { 6 } { x ^ { 2 } + 5 x + 4 }$$

A) $\frac { x ^ { 2 } - 5 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
B) $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) }$
$\frac { x ^ { 2 } + 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$
D) $\frac { x ^ { 2 } - 5 x + 24 } { ( x - 4 ) ( x + 4 ) ( x + 1 ) }$

Question 75

Perform the operation indicated. Simplify.
$$\frac { x ^ { 2 } + 7 } { x ^ { 2 } - 2 x - 15 } + \frac { 4 - 4 x } { 15 + 2 x - x ^ { 2 } }$$

A) $\frac { x + 1 } { x ^ { 2 } - 2 x - 15 }$
B) $\frac { x + 1 } { x - 5 }$
C) $\frac { x + 3 } { x - 5 }$
D) $\frac { ( x - 3 ) ( x - 1 ) } { ( x + 3 ) ( x - 5 ) }$

Question 76

Perform the operation indicated. Simplify.
$$\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + \frac { 8 } { 2 }$$

A) $\frac { 4 a + 5 b } { a + b }$
B) $\frac { 2 a b - b + 4 } { a + b + 1 }$
C) $\frac { ( a - b ) ( 4 a + 5 b ) } { a ^ { 2 } - b ^ { 2 } }$
D) $\frac { 4 a + 5 b } { a ^ { 2 } - b ^ { 2 } }$

Question 77

Perform the operation indicated. Simplify.
$$\frac { 6 x } { x + 1 } + \frac { 7 } { x - 1 } - \frac { 12 } { x ^ { 2 } - 1 }$$

A) $\frac { 6 x - 5 } { x - 1 }$
B) $\frac { 6 x } { x - 1 }$
C) $\frac { x + 1 } { x - 1 }$
D) $\frac { 6 x - 5 } { x + 1 }$

Question 78

Perform the operation indicated. Simplify.
$$\frac { 6 x + 5 } { x + 2 } - \frac { 7 x + 7 } { x + 2 } - \frac { 8 x } { x + 2 }$$

A) $\frac { x - 2 } { x + 6 }$
B) $\frac { - 21 x + 12 } { x + 2 }$
C) $\frac { - 9 x - 2 } { 3 x + 6 }$
D) $\frac { - 9 x - 2 } { x + 2 }$

Question 79

Perform the operation indicated. Simplify.
$$\frac { 20 } { x ^ { 2 } + 5 x } + \frac { 3 } { x } + \frac { 4 } { x + 5 }$$

A) $\frac { 7 } { x }$
B) $\frac { 3 } { x }$
C) $\frac { 4 } { x }$
D) $\frac { 12 } { x }$

Question 80

Perform the operation indicated. Simplify.
$$\frac { \frac { 6 } { x } + \frac { 5 } { y } } { 5 x + 6 y }$$

A) $\frac { 5 x + 6 y } { x y }$
B) $x y$
C) $\frac { 1 } { x y }$
D) $\frac { 6 x + 5 y } { 5 x + 6 y }$