Question 1

Determine the value or values that are excluded from the following expression.&#10;&#10;-$$\frac { 2 } { x - 3 }$$&#10;A)-3&#10;B)0&#10;C)3&#10;D)none

Accepted Answer

The value that is excluded from the expression $\frac { 2 } { x - 3 }$ is 3, because if $x = 3$, the denominator becomes 0, and division by 0 is undefined.

Question 2

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$&#10;A) $\{ x \mid x \neq 3 , x \neq - 3 \text {, and } x \neq - 5 \}$&#10;B) $\{ x \mid x \neq 3 \text { and } x \neq - 5 \}$&#10;C) $\{ x \mid x \neq - 3 \text { and } x \neq 5 \}$&#10;D) $\{ x \mid x \text { is a real number } \}$

Accepted Answer

$\{ x \mid x \neq 3 \text { and } x \neq - 5 \}$&#10;

Question 3

Determine the value or values that are excluded from the following expression.&#10;&#10;-$\frac { 11 x - 4 } { ( x + 7 ) ^ { 2 } }$&#10;A) $\frac { 4 } { 11 } , 7$&#10;B)7&#10;C)-7&#10;D)none

Accepted Answer

The expression is undefined when the denominator is zero. The denominator $(x + 7)^2$ is zero when $x = -7$.

Question 4

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { 1 - 2 x } { x ^ { 3 } - 20 x ^ { 2 } + 96 x }$&#10;A) $\left\{ x \mid x \neq 12 , x \neq 8 , x \neq \frac { 1 } { 2 } \text {, and } x \neq 0 \right\}$&#10;B) $\{ x \mid x \neq - 12 , x \neq 8 \text {, and } x \neq 0 \}$&#10;C) $\left\{ x \mid x \neq 12 , x \neq 8 , \text { and } x \neq \frac { 1 } { 2 } \right\}$&#10;D) $\{ x \mid x \neq 12 , x \neq 8 , \text { and } x \neq 0 \}$

Accepted Answer

The domain of the function is determined by the values of $x$ for which the denominator is not equal to zero. Factoring the denominator $x^3 - 20x^2 + 96x = x(x^2 - 20x + 96) = x(x-12)(x-8)$, we find that the denominator is zero when $x = 0$, $x = 12$, or $x = 8$. Therefore, these values must be excluded from the domain. The numerator does not introduce any additional restrictions on the domain.

Question 5

Determine the value or values that are excluded from the following expression.

- $\frac { x ^ { 2 } - 25 } { 2 x ^ { 2 } - 5 x - 7 }$

A)-5, 5
B)

- 5 , - 1 , \frac { 7 } { 2 } , 5

C)

- \frac { 7 } { 2 } , 1

D)

- 1 , \frac { 7 } { 2 }

Accepted Answer

The value that makes the denominator zero is excluded, so set $3x - 8 = 0$, solving gives $x = \frac{8}{3}$.

Question 6

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { x ^ { 3 } + 8 x ^ { 4 } } { x ^ { 2 } + 25 }$&#10;A) $\left\{ x \mid x \neq 0 \text { and } x \neq - \frac { 1 } { 8 } \right\}$&#10;B) $\{ x \mid x \neq - 5 \}$&#10;C) $\{ x \mid x \neq - 25 \}$&#10;D) $\{ \mathrm { x } \mid \mathrm { x } \text { is a real number } \}$

Accepted Answer

The denominator $x^2 + 25$ is never zero for any real number x, because $x^2$ is always non-negative and adding 25 ensures the expression is always positive. Therefore, the function is defined for all real numbers.

Question 7

Determine the domain of the function.&#10;&#10;-$g ( x ) = \frac { x + 6 } { x ^ { 2 } + 49 }$&#10;A) $\{ x \mid x \neq - 7 \text { and } x \neq 7 \}$&#10;B) $\{ x \mid x \text { is a real number } \}$&#10;C) $\{ x \mid x \neq - 7 , x \neq 7 \text {, and } x \neq - 6 \}$&#10;D) $\{ x \mid x \neq 0 \text { and } x \neq - 49 \}$

Accepted Answer

The denominator $x^2 + 49$ is always positive for all real x, because squaring any real number gives a non-negative result and adding 49 ensures it's always positive. There are no values of x that make the denominator zero, so the function is defined for all real numbers.

Question 8

Determine the value or values that are excluded from the following expression.&#10;&#10;-$\frac { x - 5 } { x ^ { 2 } - 81 }$&#10;A) $\frac { 5 } { 81 }$&#10;B)9&#10;C)9, -9&#10;D)81

Accepted Answer

The denominator $x^2 - 81$ factors into $(x + 9)(x - 9)$, so the values that make the denominator zero and are thus excluded are $x = 9$ and $x = -9$.

Question 9

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { - 2 } { 4 x + 7 }$&#10;A) $\{ x \mid x \neq 2 \}$&#10;B) $\left\{ x \mid x \neq - \frac { 7 } { 4 } \right\}$&#10;C) $\{ x \mid x \neq 0 \}$&#10;D) $\left\{ x \mid x \neq \frac { 7 } { 4 } \right\}$

Accepted Answer

The domain of the function $f(x) = \frac{-2}{4x + 7}$ is all real numbers except for the value that makes the denominator zero. Solving $4x + 7 = 0$ for $x$ gives $x = -\frac{7}{4}$, so the domain is all real numbers except $x = -\frac{7}{4}$.

Question 10

Determine the domain of the function.&#10;&#10;-$r ( x ) = \frac { x ^ { 2 } + x - 20 } { x ^ { 2 } - 14 x + 48 }$&#10;A) $\{ x \mid x \neq 5 \text { and } x \neq - 4 \}$&#10;B) $\{ x \mid x \neq 6 \text { and } x \neq 8 \}$&#10;C) $\{ x \mid x \neq - 6 \text { and } x \neq - 8 \}$&#10;D) $\{ x \mid x \neq - 5 \text { and } x \neq 4 \}$

Accepted Answer

The domain of $r(x)$ is all real numbers except those that make the denominator zero. Factoring the denominator $x^2 - 14x + 48 = (x - 6)(x - 8)$, we find that $x = 6$ and $x = 8$ make the denominator zero. Therefore, the domain excludes $x = 6$ and $x = 8$.

Question 11

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { x + 3 } { x ^ { 2 } - 1 }$&#10;A) $\{ x \mid x \neq - 1 \text { and } x \neq 1 \}$&#10;B) $\{ x \mid x \neq 0 \text { and } x \neq 1 \}$&#10;C) $\{ x \mid x \text { is a real number } \}$&#10;D) $\{ x \mid x \neq - 1 , x \neq 1 \text {, and } x \neq - 3 \}$

Accepted Answer

The answer of Determine the domain of the function.&#10;&#10;-\(f (...

Question 12

Determine the value or values that are excluded from the following expression.

- $\frac { x ^ { 2 } - 25 } { 2 x ^ { 2 } - 5 x - 7 }$

A)-5, 5
B)

- 5 , - 1 , \frac { 7 } { 2 } , 5

C)

- \frac { 7 } { 2 } , 1

D)

- 1 , \frac { 7 } { 2 }

Accepted Answer

The answer of Determine the value or values that are...

Question 13

Determine the domain of the function.&#10;&#10;-$p ( x ) = \frac { 3 x ^ { 2 } - 5 x - 2 } { x ^ { 2 } - 4 }$&#10;A) $\{ x \mid x \neq - 2 \}$&#10;B) $\{ x \mid x \neq 2 \}$&#10;C) $\{ x \mid x \text { is a real number } \}$&#10;D) $\{ x \mid x \neq 2 \text { and } x \neq - 2 \}$

Accepted Answer

The answer of Determine the domain of the function.&#10;&#10;-\(p (...

Question 14

Simplify the rational expression.&#10;&#10;-$\frac { \mathbf { r } + \mathbf { r s } } { \mathrm { r } }$&#10;A) $1 + \mathrm { rs }$&#10;B)s&#10;C)1 + s&#10;D)r + s

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { \mathbf {...

Question 15

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { 5 x - 8 } { x ^ { 2 } - 49 }$&#10;A) $\left\{ x \mid x \neq \frac { 8 } { 5 } \right\}$&#10;B) $\{ x \mid x \neq 7 \text { and } x \neq - 7 \}$&#10;C) $\{ x \mid x \neq 7 \}$&#10;D) $\{ x \mid x \neq 49 \}$

Accepted Answer

The answer of Determine the domain of the function.&#10;&#10;-\(f (...

Question 16

Determine the value or values that are excluded from the following expression.&#10;&#10;-$$\frac { 7 } { x + 8 }$$&#10;A)-8&#10;B)0&#10;C)8&#10;D)none

Accepted Answer

The answer of Determine the value or values that are...

Question 17

Determine the domain of the function.&#10;&#10;-$f ( x ) = \frac { 2 x } { x - 9 }$&#10;A) $\{ x \mid x \neq - 9 \}$&#10;B) $\{ x \mid x \neq 0 \}$&#10;C) $\{ x \mid x \text { is a real number } \}$&#10;D) $\{ x \mid x \neq 9 \}$

Accepted Answer

The answer of Determine the domain of the function.&#10;&#10;-\(f (...

Question 18

Determine the domain of the function.&#10;&#10;-$g ( x ) = \frac { x + 8 } { x ^ { 2 } + 25 x }$&#10;A) $\{ x \mid x \neq - 5 , x \neq 5 \text {, and } x \neq - 8 \}$&#10;B) $\{ x \mid x \neq - 5 \text { and } x \neq 5 \}$&#10;C) $\{ x \mid x \neq 0 \text { and } x \neq - 25 \}$&#10;D) $\{ x \mid x \text { is a real number } \}$

Accepted Answer

The answer of Determine the domain of the function.&#10;&#10;-\(g (...

Question 19

Determine the value or values that are excluded from the following expression.&#10;&#10;-$\frac { x + 5 } { x ^ { 2 } + 36 }$&#10;A)-6, -5, 6&#10;B)-6, 6&#10;C)0, -36&#10;D)none

Accepted Answer

The answer of Determine the value or values that are...

Question 20

Determine the value or values that are excluded from the following expression.&#10;&#10;-$\frac { x - 36 } { x ^ { 2 } - 7 x + 10 }$&#10;A)5, 2&#10;B)-5, -2&#10;C)6&#10;D)0

Accepted Answer

The answer of Determine the value or values that are...

Question 21

Simplify the rational expression.&#10;&#10;-$\frac { 36 - k ^ { 2 } } { k ^ { 2 } - 15 k + 54 }$&#10;A) $- \frac { \mathrm { k } + 6 } { \mathrm { k } + 9 }$&#10;B) $- \frac { k + 6 } { k - 9 }$&#10;C) $\frac { k + 6 } { k - 9 }$&#10;D) $- \frac { k - 6 } { k - 9 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 36 -...

Question 22

Simplify the rational expression.&#10;&#10;-$\frac { 22 x ^ { 2 } y ^ { 4 } - 16 x y + 4 x ^ { 5 } y ^ { 5 } } { 18 x ^ { 2 } y }$&#10;A) $\frac { 11 x y ^ { 3 } - 16 + 4 x ^ { 4 } y ^ { 4 } } { 9 x }$&#10;B) $\frac { 11 x y ^ { 3 } - 8 + 2 x ^ { 4 } y ^ { 4 } } { 9 x }$&#10;C) $\frac { 11 y ^ { 3 } - 8 + 2 x ^ { 4 } y ^ { 4 } } { 9 x }$&#10;D) $\frac { 11 y ^ { 3 } - 8 + 2 x ^ { 5 } y ^ { 5 } } { 9 x }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 22 x...

Question 23

Simplify the rational expression.&#10;&#10;-$\frac { 2 x + 2 } { 10 x ^ { 2 } + 16 x + 6 }$&#10;A) $$\frac { 1 } { 5 x + 3 }$$&#10;B) $\frac { 2 x + 5 } { 5 x + 16 }$&#10;C) $\frac { 2 x + 2 } { 10 x ^ { 2 } + 16 x + 6 }$&#10;D) $\frac { 2 x } { 5 x + 3 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 2 x...

Question 24

Simplify the rational expression.&#10;&#10;-$\frac { ( x + 3 ) ( x - 8 ) + ( x + 3 ) ( x + 7 ) } { 3 ( x + 3 ) }$&#10;A) $\frac { 2 x - 1 } { 3 }$&#10;B) $- \frac { 1 } { 3 }$&#10;C) $2 x - 1$&#10;D) $\frac { x - 1 } { 3 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { ( x...

Question 25

Simplify the rational expression.&#10;&#10;-$\frac { y ^ { 2 } + 7 y + 10 } { y ^ { 2 } + 11 y + 30 }$&#10;A) $\frac { 7 y + 1 } { 11 y + 3 }$&#10;B) $- \frac { y ^ { 2 } + 7 y + 10 } { y ^ { 2 } + 11 y + 30 }$&#10;C) $\frac { 7 y + 10 } { 11 y + 30 }$&#10;D) $\frac { y + 2 } { y + 6 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { y ^...

Question 26

Simplify the rational expression.&#10;&#10;-$\frac { y ^ { 2 } + 5 y - 24 } { y ^ { 2 } + 3 y - 40 }$&#10;A) $\frac { 5 y - 24 } { 3 y - 40 }$&#10;B)- y22 + 5 3y - 24 40&#10;C)53y - 3 5&#10;D)y - 3 5

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { y ^...

Question 27

Simplify the rational expression.&#10;&#10;-$\frac { x ^ { 2 } + 8 x + 16 } { x ^ { 2 } + 12 x + 32 }$&#10;A) $\frac { 8 x + 1 } { 12 x + 2 }$&#10;B)128x x ++ 16 32&#10;C)x x ++ 4 8&#10;D)- xx22++ 12 8x x ++ 16 32

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { x ^...

Question 28

Simplify the rational expression.&#10;&#10;-$\frac { q ^ { 3 } + 216 } { 2 q ^ { 2 } + 15 + 18 }$&#10;A) $\frac { q ^ { 2 } - 6 q + 36 } { 2 q - 3 }$&#10;B) $\frac { \mathrm { q } ^ { 2 } + 6 \mathrm { q } + 36 } { 2 \mathrm { q } - 3 }$&#10;C) $\frac { q ^ { 2 } - 6 q + 36 } { 2 q + 3 }$&#10;D) $\frac { q ^ { 2 } + 6 q - 36 } { 2 q + 3 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { q ^...

Question 29

Simplify the rational expression.&#10;&#10;-$\frac { 7 x ^ { 2 } + 21 x ^ { 3 } } { 6 x + 18 x ^ { 2 } }$&#10;A) $\frac { 7 + 21 x ^ { 3 } } { 6 x + 18 }$&#10;B) $\frac { 7 x } { 6 }$&#10;C) $\frac { 7 x ^ { 2 } + 21 x ^ { 3 } } { 6 x + 18 x ^ { 2 } }$&#10;D) $\frac { 7 } { 6 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 7 x...

Question 30

Simplify the rational expression.&#10;&#10;-$\frac { 4 x - 14 x ^ { 2 } } { 2 x }$&#10;A)0&#10;B)1&#10;C) $2 - 7 x$&#10;D) $2 + 7 x$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 4 x...

Question 31

Simplify the rational expression.&#10;&#10;-$\frac { 3 x ^ { 2 } - 27 } { 18 - 6 x }$&#10;A) $\frac { x ^ { 2 } - 9 } { 3 - x }$&#10;B) $- \frac { x + 3 } { 2 }$&#10;C) $\frac { x + 3 } { 2 }$&#10;D) $- 2 ( x + 3 )$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 3 x...

Question 32

Simplify the rational expression.&#10;&#10;-$\frac { 5 - m } { m - 5 }$&#10;A)1&#10;B)-m&#10;C)-1&#10;D)0

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 5 -...

Question 33

Simplify the rational expression.&#10;&#10;-$\frac { y ^ { 8 } - y ^ { 6 } } { y ^ { 2 } - 1 }$&#10;A) $y ^ { 2 } - 1$&#10;B) $y ^ { 6 }$&#10;C) $y ^ { 2 }$&#10;D)y

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { y ^...

Question 34

Simplify the rational expression.&#10;&#10;-$\frac { 125 x ^ { 3 } + 27 y ^ { 3 } } { 5 x + 3 y }$&#10;A) $5 x ^ { 2 } + x y + 3 y ^ { 2 }$&#10;B) $25 x ^ { 2 } + x y + 9 y ^ { 2 }$&#10;C) $25 x ^ { 2 } + 15 x y + 9 y ^ { 2 }$&#10;D) $25 x ^ { 2 } - 15 x y + 9 y ^ { 2 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 125 x...

Question 35

Simplify the rational expression.&#10;&#10;-$\frac { c ^ { 3 } - d ^ { 3 } } { c ^ { 2 } - d ^ { 2 } }$&#10;A) $\frac { c ^ { 2 } - c d + d ^ { 2 } } { c + d }$&#10;B)c+ d&#10;C) $\frac { c ^ { 2 } + c d + d ^ { 2 } } { c + d }$&#10;D) $\frac { c ^ { 2 } - c d + d ^ { 2 } } { c - d }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { c ^...

Question 36

Simplify the rational expression.&#10;&#10;-$\frac { 9 x ^ { 2 } - 79 x + 56 } { x - 8 }$&#10;A) $\frac { 1 } { x - 8 }$&#10;B) $9 x - 7$&#10;C) $\frac { 9 x ^ { 2 } - 79 x + 56 } { x - 8 }$&#10;D) $9 x ^ { 2 } - 86$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 9 x...

Question 37

Simplify the rational expression.&#10;&#10;-$\frac { 6 k - 12 } { 14 - 7 k }$&#10;A) $- \frac { 6 } { 7 }$&#10;B) $\frac { 6 } { 7 }$&#10;C)-1&#10;D)1

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { 6 k...

Question 38

Simplify the rational expression.&#10;&#10;-$\frac { m ^ { 2 } - 9 m } { 9 - m }$&#10;A)-(m + 3)&#10;B)m + 3&#10;C)-m&#10;D)m

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { m ^...

Question 39

Simplify the rational expression.&#10;&#10;-$\frac { y ^ { 3 } - 64 } { y - 4 }$&#10;A) $y ^ { 2 } + 4 y + 16$&#10;B) $y ^ { 2 } - 16$&#10;C) $\frac { 1 } { y - 4 }$&#10;D) $\frac { y ^ { 3 } - 64 } { y - 4 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { y ^...

Question 40

Simplify the rational expression.&#10;&#10;-$\frac { m ^ { 2 } - 10 m n + 24 n ^ { 2 } } { m ^ { 2 } - 8 m n + 16 n ^ { 2 } }$&#10;A) $\frac { m - 6 n } { ( m - 4 n ) ^ { 2 } }$&#10;B) $\frac { m - 4 n } { m - 6 n }$&#10;C) $\frac { m - 6 n } { m - 4 n }$&#10;D) $\frac { m - 6 } { m - 4 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { m ^...

Question 41

Multiply.&#10;&#10;-$\frac { 1 } { x + 8 } \cdot \frac { x ^ { 2 } + 18 x + 80 } { x + 10 }$&#10;A)1&#10;B) $\frac { x - 10 } { x + 8 }$&#10;C)x + 8&#10;D) $\frac { x - 8 } { x + 10 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 1 } { x +...

Question 42

Multiply.&#10;&#10;-$\frac { y ^ { 2 } - 25 } { y ^ { 2 } - 9 } \cdot \frac { y ^ { 2 } + 7 y + 12 } { y ^ { 2 } - 8 y + 15 }$&#10;A) $\frac { ( y - 5 ) ( y + 4 ) } { ( y + 3 ) ^ { 2 } }$&#10;B) $\frac { ( y + 5 ) ( y + 4 ) } { ( y + 3 ) ^ { 2 } }$&#10;C) $\frac { ( y + 5 ) ( y + 4 ) } { y - 3 }$&#10;D) $\frac { ( y + 5 ) ( y + 4 ) } { ( y - 3 ) ^ { 2 } }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { y ^ { 2 }...

Question 43

Simplify the rational expression.&#10;&#10;-$\frac { a ^ { 2 } - a b + 12 a - 12 b } { a + 12 }$&#10;A) $\frac { a ^ { 2 } - a b + 12 a - 12 b } { a + 12 }$&#10;B) $a - 2 b + 1$&#10;C)a - b&#10;D) $\frac { 1 } { a + 12 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { a ^...

Question 44

Multiply.&#10;&#10;-$\frac { 3 x y ^ { 5 } } { 5 x ^ { 6 } y ^ { 3 } } \cdot \frac { - 20 x ^ { 5 } y ^ { 8 } } { 9 x ^ { 7 } y ^ { 12 } }$&#10;A) $- \frac { 27 y ^ { 6 } } { 100 x ^ { 3 } }$&#10;B) $- \frac { 4 } { 3 x ^ { 6 } y ^ { 3 } }$&#10;C) $- \frac { 4 } { 3 x ^ { 7 } y ^ { 2 } }$&#10;D) $- \frac { 4 } { 3 x ^ { 8 } y ^ { 2 } }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 3 x y ^ {...

Question 45

Multiply.&#10;&#10;-$\frac { 6 x - 9 x ^ { 2 } } { 9 x ^ { 2 } + 24 x + 16 } \cdot \frac { 9 x ^ { 2 } + 18 x + 8 } { 9 x ^ { 2 } - 4 }$&#10;A) $\frac { 3 x } { 3 x + 4 }$&#10;B) $- \frac { 3 x } { 3 x + 4 }$&#10;C)1&#10;D) $\frac { 3 x ( 2 - 3 x ) } { 3 x + 4 ) ( 3 x - 2 ) }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 6 x - 9 x...

Question 46

Multiply.&#10;&#10;-$\frac { 4 x } { 8 x + 4 } \cdot \frac { 6 x + 3 } { 5 }$&#10;A) $\frac { 3 } { 5 }$&#10;B) $\frac { x } { 5 }$&#10;C) $\frac { 3 x } { 5 }$&#10;D) $\frac { 3 x } { 20 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 4 x } { 8...

Question 47

Multiply.&#10;&#10;-$\frac { x ^ { 3 } + x ^ { 2 } y + 3 x + 3 y } { 2 x ^ { 4 } + 6 x ^ { 2 } } \cdot \frac { 9 x ^ { 3 } } { 3 x ^ { 2 } - 3 y ^ { 2 } }$&#10;A) $\frac { 3 x ( x + y ) } { 2 ( x - y ) }$&#10;B) $\frac { 3 x } { 2 ( x + y ) }$&#10;C) $\frac { 3 x } { ( x - y ) }$&#10;D) $\frac { 3 x } { 2 ( x - y ) }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { x ^ { 3 }...

Question 48

Multiply.&#10;&#10;-$\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 9 x } { - 27 x - 27 }$&#10;A) $\frac { x + 1 } { 3 ( - x - 1 ) }$&#10;B) $- \frac { x ^ { 2 } + 1 } { 3 }$&#10;C) $- \frac { x ^ { 3 } + 1 } { 3 ( x + 1 ) }$&#10;D) $- \frac { 1 } { 3 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { x ^ { 3 }...

Question 49

Multiply.&#10;&#10;-$\frac { x - 8 } { x - 1 } \cdot \frac { 1 - x } { 8 - x }$&#10;A)- 8&#10;B)8&#10;C)-1&#10;D)1

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { x - 8 } {...

Question 50

Multiply.&#10;&#10;-$\frac { 2 z ^ { 3 } } { 3 } \cdot \frac { 18 } { z ^ { 2 } }$&#10;A) $12 \mathrm { z }$&#10;B) $\frac { 12 } { \mathrm { z } }$&#10;C) $\frac { 12 z ^ { 2 } } { z ^ { 3 } }$&#10;D) $\frac { \mathrm { z } } { 12 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 2 z ^ { 3...

Question 51

Multiply.&#10;&#10;-$\frac { 3 m ^ { 2 } + 6 m n + 3 n ^ { 2 } } { m ^ { 2 } - n ^ { 2 } } \cdot \frac { n - m } { 8 m + 8 n }$&#10;A) $\frac { 3 } { 8 ( m + n ) }$&#10;B) $\frac { 3 } { 8 }$&#10;C) $- \frac { 3 } { 8 }$&#10;D)-3

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 3 m ^ { 2...

Question 52

Multiply.&#10;&#10;-$\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 36 } \cdot \frac { x ^ { 2 } + 9 x } { x ^ { 2 } + 6 x - 16 }$&#10;A) $\frac { x } { x ^ { 2 } + 13 x + 36 }$&#10;B) $\frac { 1 } { x - 2 }$&#10;C) $\frac { x } { x - 2 }$&#10;D) $\frac { x ( x + 9 ) } { x - 2 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { x ^ { 2 }...

Question 53

Multiply.&#10;&#10;-$\frac { 3 x ^ { 2 } } { 5 } \cdot \frac { 40 } { x ^ { 3 } }$&#10;A) $\frac { 24 x ^ { 2 } } { x ^ { 3 } }$&#10;B) $\frac { 24 } { x }$&#10;C) $\frac { x } { 24 }$&#10;D) $\frac { 120 x ^ { 2 } } { 5 x ^ { 3 } }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 3 x ^ { 2...

Question 54

Simplify the rational expression.&#10;&#10;-$\frac { w ^ { 3 } - 5 w ^ { 2 } - 2 w + 10 } { w ^ { 2 } - 10 w + 25 }$&#10;A) $\frac { w + 5 } { w ^ { 2 } + 2 }$&#10;B) $\frac { w ^ { 2 } - 2 } { w - 5 }$&#10;C) $\frac { w ^ { 2 } + 2 } { w + 5 }$&#10;D) $\frac { w ^ { 2 } - 5 } { w - 2 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { w ^...

Question 55

Multiply.&#10;&#10;-$\frac { 7 y } { 14 y + 7 } \cdot \frac { 10 y + 5 } { 4 }$&#10;A) $\frac { 5 y } { 28 }$&#10;B) $\frac { y } { 4 }$&#10;C) $\frac { 5 y } { 4 }$&#10;D) $\frac { 5 } { 4 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 7 y } { 14...

Question 56

Multiply.&#10;&#10;-$\frac { x ^ { 2 } + 12 x + 32 } { x ^ { 2 } + 13 x + 40 } \cdot \frac { x ^ { 2 } + 7 x + 10 } { x ^ { 2 } + 6 x + 8 }$&#10;A) $\frac { x + 4 } { x + 5 }$&#10;B) $\frac { x + 5 } { x + 2 }$&#10;C)1&#10;D) $\frac { 1 } { x + 2 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { x ^ { 2 }...

Question 57

Multiply.&#10;&#10;-$\frac { 2 p - 2 } { p } \cdot \frac { 9 p ^ { 2 } } { 8 p - 8 }$&#10;A) $\frac { 9 p } { 4 }$&#10;B) $\frac { 16 p ^ { 2 } + 32 p + 16 } { 9 p ^ { 3 } }$&#10;C) $\frac { 18 p ^ { 3 } - 18 p ^ { 2 } } { 8 p ^ { 2 } - 8 p }$&#10;D) $\frac { 4 } { 9 p }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 2 p - 2 }...

Question 58

Simplify the rational expression.&#10;&#10;-$\frac { x ^ { 2 } + 6 x - x y - 6 y } { x ^ { 2 } - x y + 5 x - 5 y }$&#10;A) $\frac { x + 6 } { x - 5 }$&#10;B) $\frac { x + 6 } { x + 5 }$&#10;C) $\frac { 6 x - 6 y } { 5 x + 5 y }$&#10;D) $\frac { x - 6 } { x + 5 }$

Accepted Answer

The answer of Simplify the rational expression.&#10;&#10;-\(\frac { x ^...

Question 59

Multiply.&#10;&#10;-$\frac { 9 x ^ { 4 } - 72 x } { 3 x ^ { 2 } - 12 } \cdot \frac { x ^ { 2 } + x - 2 } { 4 x ^ { 3 } + 8 x ^ { 2 } + 16 x }$&#10;A) $\frac { 3 ( x - 1 ) } { 4 }$&#10;B) $\frac { 3 x ( x - 1 ) ( x - 2 ) ^ { 2 } } { 4 ( x + 2 ) ^ { 2 } }$&#10;C) $\frac { 3 x ( x + 1 ) } { 4 }$&#10;D) $\frac { 3 x ( x - 1 ) } { 4 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { 9 x ^ { 4...

Question 60

Multiply.&#10;&#10;-$\frac { z ^ { 3 } - 64 } { z ^ { 2 } - 3 z - 4 } \cdot \frac { 2 z ^ { 2 } + 11 z + 9 } { 11 z ^ { 2 } + 44 z + 176 }$&#10;A) $\frac { 2 z + 9 } { 11 }$&#10;B) $\frac { ( 2 z + 9 ) ( z + 4 ) } { 11 ( z - 4 ) }$&#10;C) $\frac { ( z + 9 ) ( z + 4 ) } { 11 ( z - 4 ) }$&#10;D) $\frac { z + 9 } { 11 }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { z ^ { 3 }...

Question 61

Divide.&#10;&#10;-$\frac { ( \mathrm { y } - 10 ) ^ { 2 } } { 8 } \div \frac { 8 \mathrm { y } - 80 } { 64 }$&#10;A) $\frac { ( \mathrm { y } - 10 ) ^ { 3 } } { 64 }$&#10;B) $\frac { 1 } { y - 10 }$&#10;C) $\frac { 8 ( y - 10 ) ^ { 2 } } { 8 y - 80 }$&#10;D)y - 10

Accepted Answer

The answer of Divide.&#10;&#10;-\(\frac { ( \mathrm { y }...

Question 62

Multiply.&#10;&#10;-$\frac { x ^ { 3 } - 3 x ^ { 2 } + 5 x - 15 } { x ^ { 5 } - 2 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } } \cdot \frac { 4 x ^ { 3 } + 8 x ^ { 2 } + x + 2 } { 4 x ^ { 3 } - 12 x ^ { 2 } + x - 3 }$&#10;A) $\frac { \left( x ^ { 2 } + 5 \right) ( x + 2 ) } { \left( x ^ { 4 } + 5 x ^ { 2 } \right) ( x - 2 ) }$&#10;B) $\frac { 1 } { x ^ { 2 } }$&#10;C) $\frac { x + 2 } { x ^ { 2 } ( x - 2 ) }$&#10;D) $\frac { 2 } { x ( x - 2 ) }$

Accepted Answer

The answer of Multiply.&#10;&#10;-\(\frac { x ^ { 3 }...

Question 63

Divide.&#10;&#10;-$\frac { 3 x ^ { 2 } } { 5 } \div \frac { x ^ { 3 } } { 20 }$&#10;A) $\frac { x } { 12 }$&#10;B) $\frac { 60 x ^ { 2 } } { 5 x ^ { 3 } }$&#10;C) $\frac { 12 x ^ { 2 } } { x ^ { 3 } }$&#10;D) $\frac { 12 } { x }$

Accepted Answer

The answer of Divide.&#10;&#10;-\(\frac { 3 x ^ { 2...

Question 64

Divide.&#10;&#10;-$\frac { x ^ { 2 } + 5 x + 6 } { x ^ { 2 } + 11 x + 18 } \div \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 18 x + 81 }$&#10;A) $\frac { x + 9 } { x ^ { 2 } + 9 x }$&#10;B) $x + 9$&#10;C) $\frac { x } { x ^ { 2 } + 11 x + 18 }$&#10;D) $\frac { x + 9 } { x }$

Accepted Answer

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

Deck 6: Rational Expressions and Equations