Question 1

Find all numbers for which the rational expression is not defined.&#10;$$\frac { 9 } { b + 8 }$$&#10;A) $b = 0$&#10;B) None&#10;C) $b = - 8$&#10;D) $b = 8$

Accepted Answer

The expression is not defined if the denominator is equal to zero. Thus, the expression is not defined when $b+8=0$, which is equivalent to $b=-8$. Therefore, the correct choice is $\boxed{	extbf{(C) } b=-8}$.

Question 2

Find all numbers for which the rational expression is not defined.&#10;$$\frac { d - 5 } { 2 - d }$$&#10;A) $d = 2,5$&#10;B) $d = - 2$&#10;C) $d = 2$&#10;D) None

Accepted Answer

The expression is undefined when the denominator equals zero. Setting $2 - d = 0$ gives $d = 2$, making option C correct.

Question 3

Multiply. Do not simplify.&#10;$$\frac { x + 5 } { x + 4 } \cdot \frac { x - 5 } { x - 5 }$$&#10;A) $\frac { x + 5 } { ( x + 4 ) ( x - 5 ) }$&#10;B) $\frac { ( x + 5 ) ( x - 5 ) } { x + 4 }$&#10;C) $\frac { ( x + 4 ) ( x - 5 ) } { ( x + 5 ) ( x - 5 ) }$&#10;D) $\frac { ( x + 5 ) ( x - 5 ) } { ( x + 4 ) ( x - 5 ) }$

Accepted Answer

To multiply, we simply multiply the terms in the numerator and denominator separately:

$$\frac { x + 5 } { x + 4 } \cdot \frac { x - 5 } { x - 5 } = \frac{(x+5)\cdot (x-5)}{(x+4)\cdot(x-5)} = \frac{(x+5)(x-5)}{(x+4)(x-5)}$$

Choice D matches this product. Choice A can be simplified by canceling the (x-5) terms, but it is generally better to leave the denominator in factored form. Choice B incorrectly distributes the (x-5) term to the denominator. Choice C can be simplified by canceling the (x-5) terms, but it is also better to leave the denominator in factored form.

Question 4

Multiply. Do not simplify.&#10;$\frac { 3 y ^ { 2 } } { 3 y ^ { 2 } } \cdot \frac { 9 z } { 8 x }$&#10;A) $\frac { \left( 3 y ^ { 2 } \right) ( 8 x ) } { \left( 3 y ^ { 2 } \right) ( 9 z ) }$&#10;B) $\frac { \left( 3 y ^ { 2 } \right) ( 9 z ) } { 8 x }$&#10;C) $\frac { \left( 3 y ^ { 2 } \right) ( 9 z ) } { \left( 3 y ^ { 2 } \right) ( 8 x ) }$&#10;D) $\frac { 9 \mathrm { z } } { \left( 3 \mathrm { y } ^ { 2 } \right) ( 8 \mathrm { x } ) }$

Accepted Answer

When multiplying fractions, we multiply the numerators and denominators separately. So, multiplying the given fractions, we get: 
$$\frac { 3 y ^ { 2 } } { 3 y ^ { 2 } } \cdot \frac { 9 z } { 8 x } = \frac{(3y^2)(9z)}{(3y^2)(8x)} = \frac{27yz}{24xy} = \frac{9z}{8x}$$ The only option that matches this is C.

Question 5

Simplify.&#10;$$\frac { 10 - 10 x } { 5 x - 5 }$$&#10;A) 2&#10;B) $10 x - 10$&#10;C) $- 2$&#10;D) $5 x - 5$

Accepted Answer

We can factor out a 10 from both the numerator and denominator to get: $$\frac{10(1-x)}{5(x-1)}=\frac{2(1-x)}{x-1}=-2\cdot\frac{1-x}{1-x}=-2$$ Notice that we can cancel out the factor of $1-x$ in the numerator and denominator, so the simplified expression is just $-2$. Therefore, the answer is choice C.

Question 6

Find all numbers for which the rational expression is not defined.
$\frac { x ^ { 2 } - 81 } { x ^ { 2 } - 7 x + 12 }$

A)

x = 0

B)

x = 9

and

x = - 9

C)

x = - 3

and

x = - 4

D)

x = 3

and

x = 4

Accepted Answer

The expression is undefined when the denominator equals zero. Factoring the denominator gives $x^2 - 7x + 12 = (x - 3)(x - 4)$, so the expression is undefined for $x = 3$ and $x = 4$.

Question 7

Simplify.&#10;$\frac { 15 x + 3 } { 9 }$&#10;A) $\frac { 5 x + 1 } { 3 }$&#10;&#1042;) $\frac { 5 x } { 3 }$&#10;C) $5 x + 1$&#10;D) $\frac { 5 x + 1 } { 9 }$

Accepted Answer

The expression $\frac { 15 x + 3 } { 9 }$ can be simplified by factoring out a common factor of 3 from the numerator, resulting in $\frac { 3(5x + 1) } { 9 }$, which simplifies further to $\frac { 5x + 1 } { 3 }$ by dividing both the numerator and the denominator by 3.

Question 8

Multiply. Do not simplify.&#10;$$\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 3 }$$&#10;A) $\frac { 3 x ( x - 9 ) } { x + 3 }$&#10;B) $\frac { x - 9 } { 3 x ( x + 3 ) }$&#10;C) $\frac { 3 x ( x - 9 ) } { 3 x ( x + 3 ) }$&#10;D) $\frac { 3 x ( x + 3 ) } { 3 x ( x - 9 ) }$

Accepted Answer

To multiply, we simply multiply across the numerators and across the denominators. Thus,
$$\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 3 } = \frac{3x(x-9)}{3x(x+3)} = \frac { 3 x ( x - 9 ) } { 3 x ( x + 3 ) }$$
We can cancel out the common factors in the numerator and the denominator, and the result is the expression in choice C.

Question 9

Find all numbers for which the rational expression is not defined.&#10;$$\frac { 2 } { a - 9 }$$&#10;A) None&#10;B) $a = 9$&#10;C) $a = - 9$&#10;D) $a = 0$

Accepted Answer

The expression is undefined when the denominator is equal to zero. Therefore, we need to solve the equation $a-9=0$ to find the value(s) of $a$ that makes the expression undefined. This gives us $a=9$. Thus, the answer is choice B, which is the only value of $a$ that makes the expression undefined.

Question 10

Multiply. Do not simplify.&#10;$\frac { 2 a + 1 } { 9 a - 1 } \cdot \frac { a } { a }$&#10;A) $\frac { ( 2 a + 1 ) a } { ( 9 a - 1 ) a }$&#10;B) $\frac { ( 2 a + 1 ) a } { 9 a - 1 }$&#10;C) $\frac { ( 9 a - 1 ) a } { ( 2 a + 1 ) a }$&#10;D) $\frac { 2 a + 1 } { ( 9 a - 1 ) a }$

Accepted Answer

When multiplying fractions, you multiply the numerators together and the denominators together. Here, $(2a + 1) \cdot a$ becomes the numerator and $(9a - 1) \cdot a$ becomes the denominator, resulting in $\frac{(2a + 1)a}{(9a - 1)a}$.

Question 11

Find all numbers for which the rational expression is not defined.
$\frac { x ^ { 2 } - 81 } { x ^ { 2 } - 7 x + 12 }$

A)

x = 0

B)

x = 9

and

x = - 9

C)

x = - 3

and

x = - 4

D)

x = 3

and

x = 4

Accepted Answer

The answer of Find all numbers for which the rational...

Question 12

Find all numbers for which the rational expression is not defined.
$\frac { x ^ { 2 } - 81 } { x ^ { 2 } - 7 x + 12 }$

A)

x = 0

B)

x = 9

and

x = - 9

C)

x = - 3

and

x = - 4

D)

x = 3

and

x = 4

Accepted Answer

The answer of Find all numbers for which the rational...

Question 13

Find all numbers for which the rational expression is not defined.
$\frac { x ^ { 2 } - 81 } { x ^ { 2 } - 7 x + 12 }$

A)

x = 0

B)

x = 9

and

x = - 9

C)

x = - 3

and

x = - 4

D)

x = 3

and

x = 4

Accepted Answer

The answer of Find all numbers for which the rational...

Question 14

Simplify.&#10;$\frac { 15 k ^ { 3 } } { 5 k }$&#10;A) $3 \mathrm { k } ^ { 2 }$&#10;B) 10&#10;C) $3 k$&#10;D) $10 \mathrm { k } ^ { 2 }$

Accepted Answer

The answer of Simplify.&#10;\(\frac { 15 k ^ { 3...

Question 15

Simplify.&#10;$\frac { 12 m ^ { 3 } p ^ { 2 } } { 6 m ^ { 8 } p }$&#10;A) $2 m ^ { 5 } p ^ { 2 }$&#10;B) $\frac { 2 m ^ { 5 } } { p }$&#10;C) $\frac { 2 p } { m ^ { 5 } }$&#10;D) $2 \mathrm { mp }$

Accepted Answer

The answer of Simplify.&#10;\(\frac { 12 m ^ { 3...

Question 16

Simplify.&#10;$$\frac { 9 x ^ { 2 } - 45 x } { 15 x ^ { 2 } - 75 x }$$&#10;A) 3&#10;B) $\frac { 5 } { 3 }$&#10;C) $\frac { 3 } { 5 }$&#10;D) $\frac { x - 5 } { 5 x - 25 }$

Accepted Answer

The answer of Simplify.&#10;\[\frac { 9 x ^ { 2...

Question 17

Find all numbers for which the rational expression is not defined.&#10;$\frac { c - 7 } { 9 }$&#10;A) None&#10;B) $c = 7$&#10;C) $\mathrm { c } = - 7$&#10;D) $\mathrm { c } = 0$

Accepted Answer

The answer of Find all numbers for which the rational...

Question 18

Simplify.&#10;$\frac { 2 m ^ { 2 } + 2 m } { 6 m ^ { 2 } + 8 m }$&#10;A) $\frac { m + 1 } { 3 m + 4 }$&#10;B) $\frac { m + 1 } { m + 4 }$&#10;C) $\frac { m + 2 } { 3 m + 4 }$&#10;D) $\frac { m ^ { 2 } + 1 } { 3 m ^ { 2 } + 4 }$

Accepted Answer

The answer of Simplify.&#10;\(\frac { 2 m ^ { 2...

Question 19

Find all numbers for which the rational expression is not defined.&#10;$$\frac { b - 6 } { 6 b - 24 }$$&#10;A) $b = 24$&#10;B) $b = 0$&#10;C) $b = 4$&#10;D) $b = - 6$

Accepted Answer

The answer of Find all numbers for which the rational...

Question 20

Multiply. Do not simplify.&#10;$$\frac { x - 4 } { 8 - x } \cdot \frac { - 1 } { - 1 }$$&#10;A) $\frac { ( x - 4 ) ( - 1 ) } { 8 - x }$&#10;B) $\frac { x - 4 } { ( 8 - x ) ( - 1 ) }$&#10;C) $\frac { ( 8 - x ) ( - 1 ) } { ( x - 4 ) ( - 1 ) }$&#10;D) $\frac { ( x - 4 ) ( - 1 ) } { ( 8 - x ) ( - 1 ) }$

Accepted Answer

The answer of Multiply. Do not simplify.&#10;\[\frac { x -...

Question 21

Find the reciprocal.&#10;$$\frac { y ^ { 2 } + 8 y + 9 } { y ^ { 2 } - y + 11 }$$&#10;A) $\frac { y ^ { 2 } + 8 y - 9 } { y ^ { 2 } - y - 11 }$&#10;B) $\frac { y ^ { 2 } - y + 11 } { y ^ { 2 } + 8 y + 9 }$&#10;C) $\frac { y ^ { 2 } - 9 y + 8 } { y ^ { 2 } + y + 11 }$&#10;D) $\frac { y ^ { 2 } - y - 11 } { y ^ { 2 } + 8 y - 9 }$

Accepted Answer

The answer of Find the reciprocal.&#10;\[\frac { y ^ {...

Question 22

Multiply and, if possible, simplify.&#10;$\frac { 3 p - 3 } { p } \cdot \frac { 8 p ^ { 2 } } { 7 p - 7 }$&#10;A) $\frac { 21 p ^ { 2 } + 42 p + 21 } { 8 p ^ { 3 } }$&#10;B) $\frac { 24 p } { 7 }$&#10;C) $\frac { 24 p ^ { 3 } - 24 p ^ { 2 } } { 7 p ^ { 2 } - 7 p }$&#10;D) $\frac { 7 } { 24 p }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\(\frac { 3...

Question 23

Multiply and, if possible, simplify.&#10;$$\frac { k ^ { 2 } + 9 k + 20 } { k ^ { 2 } + 12 k + 32 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } + 10 k + 25 }$$&#10;A) $\frac { k } { k ^ { 2 } + 12 k + 32 }$&#10;B) $\frac { \mathrm { k } } { \mathrm { k } + 5 }$&#10;C) $\frac { k ^ { 2 } + 8 k } { k + 5 }$&#10;D) $\frac { 1 } { \mathrm { k } + 5 }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\[\frac { k...

Question 24

Find the reciprocal.&#10;$\frac { x } { 2 }$&#10;A) $\frac { 1 } { 2 x }$&#10;B) $\frac { 2 } { x }$&#10;C) $1 - \frac { x } { 2 }$&#10;D) $- \frac { x } { 2 }$

Accepted Answer

The answer of Find the reciprocal.&#10;\(\frac { x } {...

Question 25

Simplify.&#10;$$\frac { y ^ { 2 } + 6 y - 16 } { y ^ { 2 } + 17 y + 72 }$$&#10;A) $\frac { 6 y + 16 } { 17 y - 17 }$&#10;B) $- \frac { y ^ { 2 } + 6 y - 16 } { y ^ { 2 } + 17 y + 72 }$&#10;C) $\frac { 6 y - 16 } { 17 y + 72 }$&#10;D) $\frac { y - 2 } { y + 9 }$

Accepted Answer

The answer of Simplify.&#10;\[\frac { y ^ { 2 }...

Question 26

Find the reciprocal.&#10;$\frac { 2 } { x ^ { 2 } + y ^ { 2 } }$&#10;A) $\frac { x ^ { 2 } + y ^ { 2 } } { 2 }$&#10;B) $- \frac { 2 } { x ^ { 2 } + y ^ { 2 } }$&#10;C) $\frac { 1 } { 2 x ^ { 2 } + y ^ { 2 } }$&#10;D) $\frac { 1 } { 2 x ^ { 2 } + 2 y ^ { 2 } x }$

Accepted Answer

The answer of Find the reciprocal.&#10;\(\frac { 2 } {...

Question 27

Simplify.&#10;$$\frac { y ^ { 2 } + 4 y - 12 } { y ^ { 2 } + 3 y - 18 }$$&#10;A) $- \frac { y ^ { 2 } + 4 y - 12 } { y ^ { 2 } + 3 y - 18 }$&#10;B) $\frac { y - 2 } { y - 3 }$&#10;C) $\frac { 4 y - 2 } { 3 y - 3 }$&#10;D) $\frac { 4 y - 12 } { 3 y - 18 }$

Accepted Answer

The answer of Simplify.&#10;\[\frac { y ^ { 2 }...

Question 28

Multiply and, if possible, simplify.&#10;$\frac { x ^ { 4 } - 1 } { x ^ { 4 } - 81 } \cdot \frac { x ^ { 2 } + 9 } { x ^ { 2 } + 1 }$&#10;A) $\frac { x + 1 } { x - 3 }$&#10;B) $\frac { x - 1 } { x + 3 }$&#10;C) $\frac { x - 1 } { x - 3 }$&#10;D) $\frac { ( x + 1 ) ( x - 1 ) } { ( x + 3 ) ( x - 3 ) }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\(\frac { x...

Question 29

Multiply and, if possible, simplify.&#10;$$\frac { k ^ { 2 } + 7 k + 12 } { k ^ { 2 } + 10 k + 24 } \cdot \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 3 k - 18 }$$&#10;A) $\frac { k ^ { 2 } + 6 k } { k - 6 }$&#10;B) $\frac { k } { k - 6 }$&#10;C) $\frac { 1 } { k - 6 }$&#10;D) $\frac { k } { k ^ { 2 } + 10 k + 24 }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\[\frac { k...

Question 30

Find the reciprocal.&#10;$\frac { t + 11 } { t - 2 }$&#10;A) $\frac { t + 2 } { t - 11 }$&#10;B) $\frac { t - 11 } { t + 2 }$&#10;C) $\frac { t - 2 } { t + 11 }$&#10;D) $\frac { 11 + t } { 2 - t }$

Accepted Answer

The answer of Find the reciprocal.&#10;\(\frac { t + 11...

Question 31

Multiply and, if possible, simplify.&#10;$\frac { 7 x ^ { 2 } } { 5 } \cdot \frac { 40 } { x ^ { 3 } }$&#10;A) $\frac { x ^ { 5 } } { 28 }$&#10;B) $\frac { x } { 28 }$&#10;C) $\frac { 56 } { x }$&#10;D) $\frac { 56 x ^ { 2 } } { x ^ { 3 } }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\(\frac { 7...

Question 32

Find the reciprocal.&#10;$$\frac { x ^ { 2 } + 12 } { 3 - x }$$&#10;A) $\frac { 3 - x } { x ^ { 2 } + 12 }$&#10;B) $\frac { x ^ { 2 } + 3 } { 12 - x }$&#10;C) $\frac { x ^ { 2 } + 12 } { x - 3 }$&#10;D) $\frac { 12 - x } { x ^ { 2 } + 3 }$

Accepted Answer

The answer of Find the reciprocal.&#10;\[\frac { x ^ {...

Question 33

Multiply and, if possible, simplify.&#10;$$\frac { x ^ { 2 } } { x ^ { 2 } - 64 } \cdot \frac { x ^ { 2 } - 13 x + 40 } { x ^ { 2 } - 5 x }$$&#10;A) $\frac { x } { x + 8 }$&#10;B) $\frac { x } { ( x + 8 ) ( x + 5 ) }$&#10;C) $\frac { x ^ { 2 } } { x + 8 }$&#10;D) $\frac { x } { x - 8 }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\[\frac { x...

Question 34

Simplify.&#10;$$\frac { y ^ { 2 } + 5 y } { y ^ { 2 } + 6 y }$$&#10;A) $\frac { y ^ { 2 } + 5 y } { y + 6 }$&#10;B) $\frac { 7 y + 10 } { 8 y + 12 }$&#10;C) $\frac { y + 5 } { y ^ { 2 } + 6 y }$&#10;D) $\frac { y + 5 } { y + 6 }$

Accepted Answer

The answer of Simplify.&#10;\[\frac { y ^ { 2 }...

Question 35

Simplify.&#10;$\frac { 4 x + 2 } { 20 x ^ { 2 } + 18 x + 4 }$&#10;A) $\frac { 4 x + 5 } { 5 x + 18 }$&#10;B) $\frac { 1 } { 5 x + 2 }$&#10;C) $\frac { 4 x } { 5 x + 2 }$&#10;D) $\frac { 4 x + 2 } { 20 x ^ { 2 } + 18 x + 4 }$

Accepted Answer

The answer of Simplify.&#10;\(\frac { 4 x + 2 }...

Question 36

Multiply and, if possible, simplify.&#10;$\frac { 2 z ^ { 3 } } { 4 } \cdot \frac { 8 } { z ^ { 2 } }$&#10;A) $\frac { 4 } { \mathrm { z } }$&#10;B) $4 \mathrm { z }$&#10;C) $\frac { z } { 4 }$&#10;D) $\frac { 4 z ^ { 2 } } { z ^ { 3 } }$

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10;\(\frac { 2...

Question 37

Find the reciprocal.&#10;$$\frac { x ^ { 2 } + 8 x y - y ^ { 2 } } { x ^ { 2 } - 7 x y + y ^ { 2 } }$$&#10;A) $\frac { x ^ { 2 } + 7 x y + y ^ { 2 } } { x ^ { 2 } - 8 x y - y ^ { 2 } }$&#10;B) $\frac { 1 } { x ^ { 2 } - 7 x y - y ^ { 2 } }$&#10;C) $\frac { x ^ { 2 } - 7 x y + y ^ { 2 } } { x ^ { 2 } + 8 x y - y ^ { 2 } }$&#10;D) $\frac { x ^ { 2 } - 8 x y + y ^ { 2 } } { x ^ { 2 } + 7 x y - y ^ { 2 } }$

Accepted Answer

The answer of Find the reciprocal.&#10;\[\frac { x ^ {...

Question 38

Simplify.&#10;$$\frac { y ^ { 2 } - 3 y - 28 } { y ^ { 2 } - 2 y - 35 }$$&#10;A) $\frac { - 3 y - 28 } { - 2 y - 35 }$&#10;B) $\frac { - 3 y - 4 } { - 2 y - 5 }$&#10;C) $- \frac { y ^ { 2 } - 3 y - 28 } { y ^ { 2 } - 2 y - 35 }$&#10;D) $\frac { y + 4 } { y + 5 }$

Accepted Answer

The answer of Simplify.&#10;\[\frac { y ^ { 2 }...

Question 39

Find the reciprocal.&#10;$\frac { 11 } { y }$&#10;A) $\frac { y } { 11 }$&#10;B) $\frac { 1 } { 11 y }$&#10;C) $- \frac { 11 } { y }$&#10;D) $1 - \frac { 11 } { y }$

Accepted Answer

The answer of Find the reciprocal.&#10;\(\frac { 11 } {...

Question 40

Find the reciprocal.&#10;$$9 y ^ { 2 } + 8 y$$&#10;A) $\frac { 1 } { 9 y ^ { 2 } + 8 y }$&#10;B) $\frac { 9 y ^ { 2 } } { 8 y }$&#10;C) $1 - \left( 9 y ^ { 2 } + 8 y \right)$&#10;D) $8 y ^ { 2 } + 9 y$

Accepted Answer

The answer of Find the reciprocal.&#10;\[9 y ^ { 2...

Question 41

Add, first finding the LCD. Simplify, if possible.
$\frac { 7 } { 12 } + \frac { 1 } { 54 }$

A)

\frac { 65 } { 108 }

B)

\frac { 4 } { 33 }

C)

\frac { 65 } { 11 }

D)

\frac { 1 } { 81 }

Accepted Answer

The answer of Add, first finding the LCD. Simplify, if...

Question 42

Divide and simplify.&#10;$$\frac { x ^ { 2 } - 25 } { x } \div \frac { 4 x + 20 } { x - 5 }$$&#10;A) $\frac { 4 x } { ( x - 5 ) ^ { 2 } }$&#10;B) $\frac { ( x - 5 ) ^ { 2 } } { 4 x }$&#10;C) $\frac { ( x - 5 ) ^ { 2 } } { x }$&#10;D) $\frac { 4 ( x + 5 ) ^ { 2 } } { x }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { x ^ {...

Question 43

Find the LCM.&#10;$50 x ^ { 5 } y , 60 x ^ { 4 } y ^ { 3 } , 30 x ^ { 2 } y ^ { 4 }$&#10;A) $300 x ^ { 5 } y ^ { 4 }$&#10;B) $60 x ^ { 5 } y$&#10;C) $150 \mathrm { x } ^ { 20 } \mathrm { y } ^ { 12 }$&#10;D) $100 x ^ { 5 } y ^ { 4 }$

Accepted Answer

The answer of Find the LCM.&#10;\(50 x ^ { 5...

Question 44

Find the LCM.&#10;54,12&#10;A) 54&#10;B) 18&#10;C) 36&#10;D) 108

Accepted Answer

The answer of Find the LCM.&#10;54,12&#10;A) 54&#10;B) 18&#10;C) 36&#10;D) 108...

Question 45

Divide and simplify.&#10;$$\frac { 4 } { y - x } \div \frac { 2 } { x - y }$$&#10;A) 2&#10;B) $\frac { 2 ( x - y ) } { y - x }$&#10;C) $- 2$&#10;D) $- 4$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { 4 } {...

Question 46

Divide and simplify.&#10;$$\frac { 4 } { 9 } \div \frac { 7 } { 2 }$$&#10;A) $\frac { 14 } { 9 }$&#10;B) $\frac { 63 } { 8 }$&#10;C) $\frac { 9 } { 14 }$&#10;D) $\frac { 8 } { 63 }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { 4 } {...

Question 47

Divide and simplify.&#10;$\frac { 2 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 12 }$&#10;A) $\frac { x ^ { 5 } } { 24 }$&#10;B) $\frac { x } { 6 }$&#10;C) $\frac { 6 x ^ { 2 } } { x ^ { 3 } }$&#10;D) $\frac { 6 } { x }$

Accepted Answer

The answer of Divide and simplify.&#10;\(\frac { 2 x ^...

Question 48

Add, first finding the LCD. Simplify, if possible.
$\frac { 7 } { 12 } + \frac { 1 } { 54 }$

A)

\frac { 65 } { 108 }

B)

\frac { 4 } { 33 }

C)

\frac { 65 } { 11 }

D)

\frac { 1 } { 81 }

Accepted Answer

The answer of Add, first finding the LCD. Simplify, if...

Question 49

Divide and simplify.&#10;$$\frac { z ^ { 2 } + 8 z + 15 } { z ^ { 2 } + 12 z + 35 } \div \frac { z ^ { 2 } + 3 z } { z ^ { 2 } + 3 z - 28 }$$&#10;A) $\frac { z } { z ^ { 2 } + 12 z + 35 }$&#10;B) $\frac { z - 4 } { z ^ { 2 } + 7 z }$&#10;C) $z - 4$&#10;D) $\frac { \mathrm { z } - 4 } { \mathrm { Z } }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { z ^ {...

Question 50

Find the LCM.&#10;$30,18,15$&#10;A) 45&#10;B) 30&#10;C) 18&#10;D) 90

Accepted Answer

The answer of Find the LCM.&#10;$30,18,15$&#10;A) 45&#10;B) 30&#10;C) 18&#10;D) 90...

Question 51

Find the LCM.&#10;$10,12,30$&#10;A) 30&#10;B) 60&#10;C) 12&#10;D) 20

Accepted Answer

The answer of Find the LCM.&#10;$10,12,30$&#10;A) 30&#10;B) 60&#10;C) 12&#10;D) 20...

Question 52

Divide and simplify.&#10;$$\frac { - 18 + 6 x } { 18 } \div \frac { 9 - 3 x } { 9 }$$&#10;A) $\frac { x - 3 } { 3 - x }$&#10;B) 1&#10;C) $\frac { x - 3 } { x + 3 }$&#10;D) $- 1$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { - 18 +...

Question 53

Divide and simplify.&#10;$$\frac { z ^ { 2 } + 7 z + 10 } { z ^ { 2 } + 12 z + 35 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 9 z + 14 }$$&#10;A) $z + 2$&#10;B) $\frac { z + 2 } { z ^ { 2 } + 7 z }$&#10;C) $\frac { z + 2 } { z }$&#10;D) $\frac { z } { z ^ { 2 } + 12 z + 35 }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { z ^ {...

Question 54

Add, first finding the LCD. Simplify, if possible.
$\frac { 7 } { 12 } + \frac { 1 } { 54 }$

A)

\frac { 65 } { 108 }

B)

\frac { 4 } { 33 }

C)

\frac { 65 } { 11 }

D)

\frac { 1 } { 81 }

Accepted Answer

The answer of Add, first finding the LCD. Simplify, if...

Question 55

Find the LCM.&#10;$500,900,450$&#10;A) 1500&#10;B) 2250&#10;C) 4500&#10;D) 900

Accepted Answer

The answer of Find the LCM.&#10;$500,900,450$&#10;A) 1500&#10;B) 2250&#10;C) 4500&#10;D) 900...

Question 56

Divide and simplify.&#10;$$\frac { a ^ { 2 } + 8 a + 12 } { a ^ { 2 } - 4 a + 4 } \div \frac { a ^ { 2 } + 12 a + 36 } { a ^ { 2 } + 5 a + 6 }$$&#10;A) $\frac { ( a + 2 ) ^ { 2 } ( a + 3 ) } { ( a - 2 ) ^ { 2 } ( a + 6 ) }$&#10;B) $\frac { ( a + 2 ) ^ { 2 } ( a + 3 ) } { ( a - 2 ) ^ { 2 } }$&#10;C) $\frac { ( a + 6 ) ^ { 3 } } { ( a - 2 ) ^ { 2 } ( a + 3 ) }$&#10;D) $- \frac { a + 3 } { a + 6 }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { a ^ {...

Question 57

Find the LCM.&#10;$72 x , 9 x ^ { 2 } , 8 x ^ { 3 }$&#10;A) $72 x ^ { 2 }$&#10;B) $72 x ^ { 3 }$&#10;C) $72 x ^ { 5 }$&#10;D) $8 x ^ { 3 }$

Accepted Answer

The answer of Find the LCM.&#10;\(72 x , 9 x...

Question 58

Divide and simplify.&#10;$$\frac { 2 p - 2 } { p } \div \frac { 3 p - 3 } { 7 p ^ { 2 } }$$&#10;A) $\frac { 14 p ^ { 3 } - 14 p ^ { 2 } } { 3 p ^ { 2 } - 3 p }$&#10;B) $\frac { 14 p } { 3 }$&#10;C) $\frac { 6 p ^ { 2 } + 12 p + 6 } { 7 p ^ { 3 } }$&#10;D) $\frac { 3 } { 14 \mathrm { p } }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { 2 p -...

Question 59

Add, first finding the LCD. Simplify, if possible.
$\frac { 7 } { 12 } + \frac { 1 } { 54 }$

A)

\frac { 65 } { 108 }

B)

\frac { 4 } { 33 }

C)

\frac { 65 } { 11 }

D)

\frac { 1 } { 81 }

Accepted Answer

The answer of Add, first finding the LCD. Simplify, if...

Question 60

Divide and simplify.&#10;$$\frac { x ^ { 2 } + 9 x + 14 } { x + 7 } \div \frac { x ^ { 2 } - 4 } { 7 x - 14 }$$&#10;A) 7&#10;B) $\frac { 1 } { 7 }$&#10;C) $\frac { 7 x - 14 } { x - 2 }$&#10;D) $\frac { ( x + 2 ) ^ { 2 } } { 7 }$

Accepted Answer

The answer of Divide and simplify.&#10;\[\frac { x ^ {...

Question 61

Add. Simplify, if possible.&#10;$$\frac { m ^ { 2 } - 9 m } { m - 3 } + \frac { 18 } { m - 3 }$$&#10;A) $m - 3$&#10;B) $\frac { m ^ { 2 } - 9 m + 18 } { m - 3 }$&#10;C) $m + 6$&#10;D) $m - 6$

Accepted Answer

The answer of Add. Simplify, if possible.&#10;\[\frac { m ^...

Question 62

Find the LCM.&#10;$$\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }$$&#10;A) $81 \mathrm { n } ^ { 2 }$&#10;B) $n ^ { 2 } + 81$&#10;C) $n + 9$&#10;D) $n ( 9 + n ) ( 9 - n )$

Accepted Answer

The answer of Find the LCM.&#10;\[\mathrm { n } ,...

Question 63

Add. Simplify, if possible.&#10;$$\frac { 2 } { 15 x } + \frac { 5 } { 15 x }$$&#10;A) $\frac { 7 } { 15 x }$&#10;B) $\frac { 7 } { 30 x }$&#10;C) $\frac { 15 x } { 7 }$&#10;D) 1

Accepted Answer

The answer of Add. Simplify, if possible.&#10;\[\frac { 2 }...

Question 64

Add. Simplify, if possible.&#10;$$\frac { 2 } { x - 8 } + \frac { 5 } { 8 - x }$$&#10;A) $\frac { 7 } { x - 8 }$&#10;B) $\frac { - 3 } { x - 8 }$&#10;C) $\frac { 10 } { x - 8 }$&#10;D) $\frac { 3 } { x - 8 }$

Accepted Answer

The answer of Add. Simplify, if possible.&#10;\[\frac { 2 }...

Deck 6: Rational Expressions and Equations