Deck 7: Rational Expressions

Question 1

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { 6 y - 4 } { y ^ { 2 } - 9 }$$

A) $y = \frac { 2 } { 3 }$
B) $y = 9$
C) $y = 3 , y = - 3$
D) $y = 3$

Answer 1

$y = 3 , y = - 3$

Question 2

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { 4 x ^ { 2 } - 16 } { 6 x - 42 }$$

A) $x = 2 , x = - 2$
B) $x = 7$
C) $x = 42$
D) Defined for all real numbers

Answer 2

$x = 7$

Question 3

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { x ^ { 3 } + 5 x ^ { 4 } } { x ^ { 2 } + 36 }$$

A) $x = - 36$
B) $x = 0 , x = - \frac { 1 } { 5 }$
C) $x = - 6$
D) Defined for all real numbers

Answer 3

Defined for all real numbers

Question 4

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x + 2 } { x - 9 }$$

A) $\frac { 2 } { 9 }$
B) $- \frac { 2 } { 9 }$
C) cannot be simplified
D) 1

Question 5

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { 7 x ^ { 3 } } { 14 x ^ { 8 } }$

A) $\frac { x ^ { 5 } } { 2 }$
B) $\frac { 1 } { 2 x ^ { 5 } }$
C) $\frac { 1 } { 2 x ^ { 11 } }$
D) $\frac { 1 } { 2 }$

Question 6

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 5 y - 30 } { y - 6 }$$

A) cannot be simplified
B) 5
C) $\frac { 1 } { 5 }$
D) $5 y - 6$

Question 7

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { 6 } { 19 x }$$

A) $x = - 19$
B) $x = 6$
C) $x = 0$
D) Defined for all real numbers

Question 8

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { 4 } { r - 4 }$$

A) $\mathrm { r } = 4$
B) $r = 0$
C) $r = - 4$
D) Defined for all real numbers

Question 9

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 6 x - 18 } { 15 - 5 x }$$

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

Question 10

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { x + 2 } { ( x + 7 ) ( x - 3 ) }$$

A) $x = - 2$
B) $x = - 7 , x = 3$
C) $x = - 2 , x = - 7 , x = 3$
D) Defined for all real numbers

Question 11

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { x - 2 } { 4 }$$

A) $x = 2$
B) $x = - 2$
C) $x = 0$
D) Defined for all real numbers

Question 12

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { 3 x - 12 } { 27 }$

A) $\frac { x + 12 } { 9 }$
B) $\frac { x + 4 } { 9 }$
C) $\frac { x - 4 } { 9 }$
D) $\frac { x - 12 } { 9 }$

Question 13

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { - 14 } { 2 x - 10 }$

A) $- \frac { 7 } { x - 5 }$
B) $\frac { 7 } { x - 5 }$
C) $- \frac { 7 } { x + 5 }$
D) $- \frac { 7 } { x - 10 }$

Question 14

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { 6 } { a + 3 }$$

A) $a = - 3$
B) $a = 0$
C) $a = 3$
D) Defined for all real numbers

Question 15

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { a - 3 } { 7 - a }$$

A) $a = 7 , a = 3$
B) $a = 7$
C) $a = - 7$
D) Defined for all real numbers

Question 16

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
$$\frac { x ^ { 2 } - 64 } { x ^ { 2 } + 17 x + 70 }$$

A) $x = 8 , x = - 8$
B) $x = 7 , x = - 10$
C) $x = - 7 , x = - 10$
D) $x = 0$

Question 17

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { 24 x ^ { 3 } } { 6 x }$

A) 18
B) $4 x ^ { 2 }$
C) $18 x ^ { 2 }$
D) $4 \mathrm { x }$

Question 18

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 21 x - 15 } { 5 - 7 x }$$

A) cannot be simplified
B) 3
C) $- 3$
D) $- \frac { 1 } { 3 }$

Question 19

Find all values that make the rational expression undefined. If the rational expression is defined for all real numbers, so
state.
x² - 16 x² - 11x + 28

A) x = 0
B) x = -7, x = -4
C) x = 4, x = -4
D) x = 7, x = 4

Question 20

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 27 x - 24 } { 8 x - 9 x ^ { 2 } }$$

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

Question 21

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { 2 x + 3 } { 10 x ^ { 2 } + 21 x + 9 }$

A) $\frac { 2 x } { 5 x + 3 }$
B) $\frac { 1 } { 5 x + 3 }$
C) $\frac { 2 x + 5 } { 5 x + 21 }$
D) cannot be simplified

Question 22

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 2 } - 16 } { x ^ { 2 } + 8 x + 16 }$$

A) $\frac { 4 } { 8 x + 4 }$
B) $\frac { x + 4 } { x + 4 }$
C) $- 1$
D) $\frac { x - 4 } { x + 4 }$

Question 23

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 6 - x } { x - 6 }$$

A) cannot be simplified
B) 1
C) $- 1$
D) $- \mathrm { m }$

Question 24

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { ( x - 6 ) ^ { 2 } } { x ^ { 2 } - 36 }$

A) $\frac { x - 6 } { x + 6 }$
B) $\frac { x + 6 } { x - 6 }$
C) cannot be simplified
D) 1

Question 25

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 2 } - 16 } { 4 - x }$$

A) $- x + 4$
B) $x - 4$
C) $- x - 4$
D) cannot be simplified

Question 26

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 3 x - 5 } { 5 - 3 x }$$

A) 1
B) $- 1$
C) $- \frac { 3 } { 5 }$
D) cannot be simplified

Question 27

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 4 x - 8 } { x ^ { 2 } - 5 x + 6 }$$

A) $\frac { 4 } { x + 3 }$
B) cannot be simplified
C) $\frac { 4 ( x - 8 ) } { x + 3 }$
D) $\frac { 4 } { x - 3 }$

Question 28

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { y ^ { 3 } - 343 } { y - 7 }$$

A) cannot be simplified
B) $y ^ { 2 } - 49$
C) $y ^ { 2 } + 7 y + 49$
D) $\frac { 1 } { y - 7 }$

Question 29

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 3 x ^ { 2 } + 9 x ^ { 3 } } { 2 x + 6 x ^ { 2 } }$$

A) $\frac { 3 x } { 2 }$
B) cannot be simplified
C) $\frac { 3 } { 2 }$
D) $\frac { 3 + 9 x ^ { 3 } } { 2 x + 6 }$

Question 30

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { y ^ { 2 } + 7 y + 10 } { y ^ { 2 } + 10 y + 25 }$$

A) cannot be simplified
B) $\frac { 7 y + 2 } { 10 y + 5 }$
C) $\frac { y + 2 } { y + 5 }$
D) $\frac { 7 y + 10 } { 10 y + 25 }$

Question 31

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 7 x ^ { 2 } - 57 x + 8 } { x - 8 }$$

A) $7 x ^ { 2 } - 58$
B) $\frac { 1 } { x - 8 }$
C) cannot be simplified
D) $7 x - 1$

Question 32

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 81 - x ^ { 2 } } { x ^ { 2 } - 13 x + 36 }$$

A) $- \frac { x + 9 } { x + 4 }$
B) $- \frac { x - 9 } { x - 4 }$
C) $- \frac { x + 9 } { x - 4 }$
D) $\frac { x + 9 } { x - 4 }$

Question 33

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x + 12 } { x ^ { 2 } + 5 x - 84 }$$

A) $x - 7$
B) cannot be simplified
C) $\frac { 1 } { x - 7 }$
D) $\frac { 1 } { x + 7 }$

Question 34

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { y ^ { 2 } - 10 y + 24 } { 4 - y }$$

A) $- y + 6$
B) $y + 6$
C) $- y - 6$
D) $y - 6$

Question 35

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 2 } - x y + 9 x - 9 y } { x + 9 }$$

A) $x - 2 y + 1$
B) $\frac { 1 } { x + 9 }$
C) cannot be simplified
D) $x - y$

Question 36

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 3 } - x ^ { 2 } + 3 x - 3 } { x - 1 }$$

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

Question 37

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 2 } + 6 x + 4 } { x ^ { 2 } + 7 x + 12 }$$

A) $x + 2$
B) $\frac { x + 2 } { x + 3 }$
C) $\frac { x + 2 } { x + 4 }$
D) cannot be simplified

Question 38

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { 2 x - 9 } { 2 x - 1 }$$

A) cannot be simplified
B) 9
C) $\frac { 2 } { x - 1 }$
D) 2

Question 39

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { x - 5 } { x ^ { 2 } - 25 }$

A) $\frac { 1 } { x + 5 }$
B) $x + 5$
C) $\frac { 1 } { x - 5 }$
D) cannot be simplified

Question 40

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$\frac { x + 3 } { x ^ { 2 } + 9 }$

A) $\frac { 1 } { x - 3 }$
B) $\frac { 1 } { x + 3 }$
C) cannot be simplified
D) $\frac { 1 } { 3 }$

Question 41

Multiply. Simplify if possible.
$$\frac { k ^ { 2 } + 13 k + 36 } { k ^ { 2 } + 11 k + 18 } \cdot \frac { k ^ { 2 } + 4 k + 4 } { k ^ { 2 } + 6 k + 8 }$$

A) 1
B) $\frac { k + 4 } { k + 2 }$
C) $\frac { k + 2 } { k + 2 }$
D) $\frac { 1 } { k + 2 }$

Question 42

Multiply. Simplify if possible.
$$\frac { x ^ { 2 } - 5 x + 6 } { x ^ { 2 } - 11 x + 10 } \cdot \frac { x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 12 x + 27 }$$

A) $\frac { ( x + 2 ) ( x + 8 ) } { ( x + 10 ) ( x + 9 ) }$
B) $\frac { ( x - 2 ) } { ( x - 9 ) }$
C) $\frac { ( x - 2 ) ( x - 8 ) } { ( x - 10 ) ( x - 9 ) }$
D) $\frac { \left( x ^ { 2 } - 5 x + 6 \right) \left( x ^ { 2 } - 9 x + 8 \right) } { \left( x ^ { 2 } - 11 x + 10 \right) \left( x ^ { 2 } - 12 x + 27 \right) }$

Question 43

Multiply. Simplify if possible.
$$\frac { 6 y } { 12 y + 6 } \cdot \frac { 14 y + 7 } { 6 }$$

A) $\frac { 7 } { 6 }$
B) $\frac { 7 y } { 36 }$
C) $\frac { 7 y } { 6 }$
D) $\frac { y } { 6 }$

Question 44

Multiply. Simplify if possible.
$$\frac { 2 p - 2 } { p } \cdot \frac { 7 p ^ { 2 } } { 6 p - 6 }$$

A) $\frac { 12 p ^ { 2 } + 24 p + 12 } { 7 p ^ { 3 } }$
B) $\frac { 14 p ^ { 3 } - 14 p ^ { 2 } } { 6 p ^ { 2 } - 6 p }$
C) $\frac { 7 p } { 3 }$
D) $\frac { 3 } { 7 \mathrm { p } }$

Question 45

Multiply. Simplify if possible.
$$\frac { ( y - w ) ^ { 2 } } { y + w } \cdot \frac { y } { y ^ { 2 } - y w }$$

A) $\frac { y - w } { y + w }$
B) 1
C) $\frac { w } { y + w }$
D) $\frac { y + w } { y - w }$

Question 46

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 2 } - 2 x + 6 x - 12 } { 2 x ^ { 2 } + 9 x + 12 x + 54 }$$

A) $\frac { x ^ { 2 } - 8 x - 12 } { 2 x ^ { 2 } + 21 x + 54 }$
B) $\frac { x - 2 } { x + 6 }$
C) $\frac { x - 2 } { 2 x + 9 }$
D) $\frac { x + 6 } { 2 x + 9 }$

Question 47

Provide an appropriate response.
A formula for the focal length of a lens is $$f = \frac { a b } { b + a }$$ Calculate f (the focal length) for a = 8 cm and b = 17 cm. Round to the nearest tenth.

A) 2.6 cm
B) 4.0 cm
C) 8.5 cm
D) 5.4 cm

Question 48

Multiply. Simplify if possible.
$\frac { 2 x ^ { 2 } } { 3 } \cdot \frac { 21 } { x ^ { 3 } }$

A) $\frac { 14 } { x }$
B) $\frac { 14 x ^ { 2 } } { x ^ { 3 } }$
C) $\frac { x } { 14 }$
D) $\frac { 42 x ^ { 2 } } { 3 x ^ { 3 } }$

Question 49

Multiply. Simplify if possible.

- $$\frac { w ^ { 2 } - s ^ { 2 } } { w + s } \cdot \frac { w } { w ^ { 2 } - w s }$$

A) 1
B) $w$
C) $- \frac { 1 } { w }$
D) $- W$

Question 50

Multiply. Simplify if possible.
$$\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 16 k + 63 } \cdot \frac { k ^ { 2 } + 9 k } { k ^ { 2 } + 9 k + 20 }$$

A) $\frac { 1 } { k + 4 }$
B) $\frac { k } { k ^ { 2 } + 16 k + 63 }$
C) $\frac { k ^ { 2 } + 9 k } { k + 4 }$
D) $\frac { k } { k + 4 }$

Question 51

Multiply. Simplify if possible.
$\frac { 3 z ^ { 3 } } { 5 } \cdot \frac { 10 } { z ^ { 2 } }$

A) $\frac { z } { 6 }$
B) $\frac { 6 z ^ { 2 } } { z ^ { 3 } }$
C) $6 z$
D) $\frac { 6 } { \mathrm { z } }$

Question 52

Multiply. Simplify if possible.
$$\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$$

A) $\frac { 3 ( x - 1 ) } { 4 }$
B) $\frac { 3 x ( x + 1 ) } { 4 }$
C) $\frac { 3 x ( x - 1 ) } { 4 }$
D) $\frac { 3 x ( x - 1 ) ( x - 2 ) ^ { 2 } } { 4 ( x + 2 ) ^ { 2 } }$

Question 53

Provide an appropriate response.
The rational expression $$\frac { 120 x } { 100 - x }$$ describes the cost, in millions of dollars, to inoculate x percent of the current population of cattle against a particular virus. Choose which of the following statements are true with regard to this mathematical
Model.
I. The expression will be undefined when x = 100.
II. The cost of inoculating 80 percent of cattle is 200 million dollars more than the cost of inoculating 70 percent of
Cattle.
III. This expression will calculate inoculation costs for any population of cattle, no matter what the size.

A) Only I and III are true.
B) All three statements are true.
C) Only I and II are true.
D) Only II and III are true.

Question 54

Provide an appropriate response.
A tennis racket company has manufacturing costs given by the equation C = 30x + 30,000x where x is the number of rackets manufactured and C is the cost to manufacture each racket.
What number of rackets must be manufactured to bring the cost per racket to $3?

A) No number of rackets manufactured satisfies this goal.
B) Not enough information is given to answer this question.
C) 30,000 rackets
D) 33,000 rackets

Question 55

Multiply. Simplify if possible.
$$\frac { \mathrm { k } ^ { 2 } + 6 \mathrm { k } + 9 } { \mathrm { k } ^ { 2 } + 10 \mathrm { k } + 21 } \cdot \frac { \mathrm { k } ^ { 2 } + 7 \mathrm { k } } { \mathrm { k } ^ { 2 } - 5 \mathrm { k } - 24 }$$

A) $\frac { \mathrm { k } } { \mathrm { k } - 8 }$
B) $\frac { k } { k ^ { 2 } + 10 k + 21 }$
C) $\frac { \mathrm { k } ^ { 2 } + 7 \mathrm { k } } { \mathrm { k } - 8 }$
D) $\frac { 1 } { \mathrm { k } - 8 }$

Question 56

Provide an appropriate response.
A snowboard company has manufacturing costs given by the equation $$C = \frac { \mathrm { Tx } + 1000 \mathrm {~T} } { \mathrm { x } }$$ where T is a different constant for each model, x is the number of snowboards manufactured, and C is the cost to manufacture one snowboard of a particular model. Choose which of the following statements are true with
Regard to this mathematical model.
I. The manufacturing cost per snowboard is the same for all models if 8000 of each model is manufactured.
II. The manufacturing cost per snowboard decreases for all models as the number manufactured increases.
III. The manufacturing cost per snowboard decreases for only some models as the number manufactured increases.

A) Only II is true.
B) All three statements are true.
C) Only I and III are true.
D) Only I and II are true.

Question 57

Multiply. Simplify if possible.
$5 x ^ { 4 } \cdot \frac { x ^ { 2 } y } { 45 x ^ { 3 } y ^ { 2 } }$

A) $\frac { 1 } { 45 x y }$
B) $\frac { x ^ { 5 } } { 9 y }$
C) $\frac { x ^ { 6 } y } { 9 x ^ { 3 } y ^ { 2 } }$
D) $\frac { x ^ { 3 } } { 9 y }$

Question 58

Multiply. Simplify if possible.
$$\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 7 x } { - 35 x - 35 }$$

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

Question 59

Simplify the rational expression. If the rational expression cannot be simplified, so state.
$$\frac { x ^ { 2 } + 11 x y + 18 y ^ { 2 } } { x ^ { 2 } + 16 x y + 63 y ^ { 2 } }$$

A) $\frac { x + 2 y } { x + 7 y }$
B) $\frac { 11 x + 18 y } { 16 x + 63 y }$
C) cannot be simplified
D) $\frac { x + 7 y } { x + 2 y }$

Question 60

Provide an appropriate response.
A gas law in chemistry says that $$\frac { \mathrm { PV } } { \mathrm { T } } = \frac { \mathrm { pv } } { \mathrm { t } } . \text { If } \mathrm { T } = 290 , \mathrm { t } = 380 , \mathrm {~V} = 10 , \mathrm { P } = 90 , \text { and } \mathrm { v } = 8$$ , find the value of p. Round to the nearest thousandth.

A) 14.741
B) 147.414
C) 1012.5
D) 0.388

Question 61

Perform the indicated operation. Simplify if possible.
$$\frac { 9 } { 15 x } + \frac { 5 } { 15 x }$$

A) $\frac { 15 x } { 14 }$
B) $\frac { 14 } { 15 x }$
C) $\frac { 14 } { 30 x }$
D) 1

Question 62

Divide. Simplify if possible.
$$\frac { 3 y - 3 } { y } \div \frac { 5 y - 5 } { 8 y ^ { 2 } }$$

A) $\frac { 24 y ^ { 3 } - 24 y ^ { 2 } } { 5 y ^ { 2 } - 5 y }$
B) $\frac { 5 } { 24 y }$
C) $\frac { 24 y } { 5 }$
D) $\frac { 15 y ^ { 2 } + 30 y + 15 } { 8 y ^ { 3 } }$

Question 63

Divide. Simplify if possible.
$$\frac { x ^ { 2 } - 10 x + 25 } { 3 x - 15 } \div \frac { 6 x - 30 } { 18 }$$

A) $\frac { x ^ { 2 } - 10 x + 25 } { ( x - 5 ) ^ { 2 } }$
B) $\frac { ( x - 5 ) ^ { 2 } } { 9 }$
C) 1
D) 18

Question 64

Perform the indicated operations. Simplify if possible.
$$\left( \frac { 3 x ^ { 2 } - 4 x - 4 } { x ^ { 2 } + 2 x - 3 } \cdot \frac { x ^ { 2 } + 3 x - 4 } { 12 x ^ { 2 } + 11 x + 2 } \right) \div \frac { 3 x ^ { 2 } - 5 x - 2 } { 8 x ^ { 2 } - 2 x - 1 }$$

A) 1
B) $\frac { ( x + 4 ) } { ( x + 3 ) }$
C) $\frac { 3 x + 1 } { 2 x - 1 }$
D) $\frac { ( x + 4 ) ( 2 x - 1 ) } { ( x + 3 ) ( 3 x + 1 ) }$

Question 65

Divide. Simplify if possible.
$$\frac { 3 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 16 }$$

A) $\frac { x } { 12 }$
B) $\frac { 12 } { x }$
C) $\frac { 48 x ^ { 2 } } { 4 x ^ { 3 } }$
D) $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$

Question 66

Perform the indicated operation. Simplify if possible.
$$\frac { x } { 13 } + \frac { 6 } { 13 }$$

A) $\frac { 6 x } { 13 }$
B) $\frac { x + 6 } { 13 }$
C) $\frac { x + 6 } { 26 }$
D) $\frac { 6 x } { 26 }$

Question 67

Divide. Simplify if possible.
$$\frac { 15 x ^ { 2 } - 37 x y + 20 y ^ { 2 } } { 35 x ^ { 2 } - 43 x y + 12 y ^ { 2 } } + \frac { 15 x ^ { 2 } - 31 x y + 10 y ^ { 2 } } { 30 x ^ { 2 } + 23 x y - 14 y ^ { 2 } }$$

A) $\frac { ( 7 x + 3 y ) } { ( 6 x - 7 y ) }$
B) $\frac { ( 3 x - 5 y ) ^ { 2 } } { ( 6 x + 7 y ) ( 7 x - 3 y ) }$
C) $\frac { 6 x + 7 y } { 7 x - 3 y }$
D) $\frac { ( 3 x + 5 y ) ^ { 2 } } { ( 6 x - 7 y ) ( 7 x + 3 y ) }$

Question 68

Divide. Simplify if possible.
$$\frac { x ^ { 2 } + 16 x + 63 } { x ^ { 2 } + 18 x + 81 } + \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 2 x - 63 }$$

A) $\frac { x } { x ^ { 2 } + 18 x + 81 }$
B) $\frac { x - 7 } { x ^ { 2 } + 9 x }$
C) $x - 7$
D) $\frac { x - 7 } { x }$

Question 69

Divide. Simplify if possible.
$$( x + 2 ) \div \frac { x ^ { 2 } - 5 x + 6 } { 3 - x }$$

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

Question 70

Divide. Simplify if possible.
$\frac { 24 x ^ { 4 } } { x ^ { 2 } - 1 } \div \frac { x ^ { 6 } } { ( x + 1 ) ^ { 2 } }$

A) $\frac { 24 x ^ { 24 } } { ( x - 1 ) ( x + 1 ) ^ { 3 } }$
B) $\frac { 4 ( x + 1 ) } { x ^ { 2 } ( x - 1 ) }$
C) $\frac { 24 ( x + 1 ) } { x ^ { 2 } ( x - 1 ) }$
D) $\frac { 24 x ^ { 2 } ( x + 1 ) } { ( x - 1 ) }$

Question 71

Perform the indicated operation. Simplify if possible.
$$\frac { x + 5 } { 13 } + \frac { 7 } { 13 }$$

A) $\frac { x + 12 } { 26 }$
B) $\frac { 12 x } { 26 }$
C) $\frac { 12 x } { 13 }$
D) $\frac { x + 12 } { 13 }$

Question 72

Divide. Simplify if possible.
$$\frac { x ^ { 2 } - 12 x + 27 } { 3 - x } \div ( x + 9 )$$

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

Question 73

Perform the indicated operation. Simplify if possible.
$$\frac { 3 x } { 13 } + \frac { 8 x } { 13 }$$

A) $\frac { 13 x } { 11 }$
B) $\frac { 11 x ^ { 2 } } { 13 }$
C) $\frac { 11 \mathrm { x } } { 26 }$
D) $\frac { 11 \mathrm { x } } { 13 }$

Question 74

Divide. Simplify if possible.
$$\frac { x ^ { 2 } - 2 x + x y - 2 y } { 9 x ^ { 2 } - 9 y ^ { 2 } } \div \frac { x - 2 } { 12 x - 12 y }$$

A) $\frac { 12 \left( x ^ { 2 } - 2 x + x y - 2 y \right) } { 9 ( x + y ) ( x - 2 ) }$
B) 1
C) $\frac { 4 } { 3 }$
D) $\frac { ( x - 2 ) ^ { 2 } } { 108 ( x - y ) ^ { 2 } }$

Question 75

Divide. Simplify if possible.
$$\frac { 7 y + 14 } { 5 x + 25 } \div \frac { x y - 5 y + 2 x - 10 } { x ^ { 2 } - 10 x + 25 }$$

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

Question 76

Divide. Simplify if possible.
$$\frac { r ^ { 2 } - y ^ { 2 } } { r + y } \div \frac { r } { r ^ { 2 } + r y }$$

A) $r - y$
B) $r ^ { 2 } - y ^ { 2 }$
C) $- \frac { 1 } { r }$
D) $r$

Question 77

Divide. Simplify if possible.
$$\frac { 12 x - 12 } { 5 } \div \frac { 4 x - 4 } { 35 }$$

A) $\frac { 48 ( x - 1 ) ^ { 2 } } { 175 }$
B) 21
C) $\frac { 1 } { 21 }$
D) $\frac { 7 ( 12 x - 12 ) } { 4 x - 4 }$

Question 78

Perform the indicated operations. Simplify if possible.
$$\left( \frac { 9 x ^ { 2 } + 50 x - 24 } { 8 x - 16 } \cdot \frac { x ^ { 2 } - 2 x } { 81 x ^ { 2 } - 16 } \right) \div \frac { 6 x + 36 } { 7 x ^ { 3 } }$$

A) $\frac { 7 x ^ { 4 } } { 48 ( 9 x + 4 ) }$
B) $\frac { 48 } { 7 x ^ { 4 } ( 9 x + 4 ) }$
C) $\frac { 6 ( x + 6 ) ^ { 2 } } { 56 x ^ { 2 } ( 9 x + 4 ) }$
D) $\frac { 7 x ^ { 3 } } { 48 ( 9 x + 4 ) }$

Question 79

Divide. Simplify if possible.
$$\frac { ( y - 5 ) ^ { 2 } } { 3 } \div \frac { 3 y - 15 } { 9 }$$

A) $\frac { 3 ( y - 5 ) ^ { 2 } } { 3 y - 15 }$
B) $\frac { ( y - 5 ) ^ { 3 } } { 9 }$
C) $y - 5$
D) $\frac { 1 } { y - 5 }$

Question 80

Perform the indicated operation. Simplify if possible.
$$\frac { 15 x } { 4 } + \frac { 15 x } { 4 }$$

A) $\frac { 15 x ^ { 2 } } { 2 }$
B) $\frac { 2 } { 15 x }$
C) $\frac { 15 x } { 4 }$
D) $\frac { 15 x } { 2 }$