Question 1

Find all numbers for which the rational expression is not defined.&#10; &#10;A)b = 0&#10;B)b = 4&#10;C)b = -4&#10;D)None

Accepted Answer

A rational expression is not defined when its denominator is equal to zero. In this case, the denominator is $b + 4$. Setting $b + 4 = 0$ gives $b = -4$, which means the expression is undefined for $b = -4$.

Question 2

Find a linear function whose graph has the given slope and y-intercept.&#10;

Accepted Answer

When multiplying fractions, you multiply the numerators together and the denominators together. Here, multiplying $\frac{6a+1}{3a-1}$ by $\frac{a}{a}$ results in $\frac{(6a+1)a}{(3a-1)a}$, which matches choice A.

Question 3

Multiply. Do not simplify.&#10;

Accepted Answer

The expression simplifies to $\frac{2}{3}$ by factoring out common terms in the numerator and denominator and then reducing.

Question 4

Find all numbers for which the rational expression is not defined.&#10; &#10;A)c = 2&#10;B)None&#10;C)c = 0&#10;D)c = -2

Accepted Answer

The expression $\frac{c - 2}{3}$ is defined for all real numbers because the denominator is a constant (3) and does not depend on the variable $c$.

Question 5

Find all numbers for which the rational expression is not defined.&#10; &#10;A)None&#10;B)a = 0&#10;C)a = -5&#10;D)a = 5

Accepted Answer

The expression is undefined when the denominator equals zero, which occurs when $a - 5 = 0$, or $a = 5$.

Question 6

Find all numbers for which the rational expression is not defined.&#10; &#10;A)d = 4&#10;B)d = -4&#10;C)d = 4, 7&#10;D)None

Accepted Answer

The expression is undefined when the denominator equals zero, which happens when $d = 4$.

Question 7

Multiply. Do not simplify.&#10;

Accepted Answer

Factor the numerator and cancel the common factor of 3.

Question 8

Find a linear function whose graph has the given slope and y-intercept.&#10;

Accepted Answer

The correct multiplication of the given fractions $\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 10 }$ simplifies to $\frac { 3 x ( x - 9 ) } { 3 x ( x + 10 ) }$, as the numerator and denominator are multiplied separately.

Question 9

Find all numbers for which the rational expression is not defined.&#10;

Accepted Answer

The rational expression is undefined when the denominator is equal to zero. Factoring the denominator $x^2 - 3x - 10$ gives $(x - 5)(x + 2) = 0$, so the expression is undefined for $x = 5$ and $x = -2$.

Question 10

Find all numbers for which the rational expression is not defined.&#10;x2 - 16 x2 - 16x + 63&#10;A)x = 4 and x = -4&#10;B)x = 0&#10;C)x = -9 and x = -7&#10;D)x = 9 and x = 7

Accepted Answer

The rational expression is undefined when the denominator is equal to zero. Factoring the denominator $x^2 - 16x + 63$ gives $(x - 9)(x - 7)$. Setting each factor equal to zero gives $x = 9$ and $x = 7$, so the expression is undefined for $x = 9$ and $x = 7$.

Question 11

Find all numbers for which the rational expression is not defined.&#10;

Accepted Answer

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

Question 12

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 13

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 14

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 15

Find a linear function whose graph has the given slope and y-intercept.&#10;

Accepted Answer

The answer of Find a linear function whose graph has...

Question 16

Find a linear function whose graph has the given slope and y-intercept.&#10;

Accepted Answer

The answer of Find a linear function whose graph has...

Question 17

Find a linear function whose graph has the given slope and y-intercept.&#10;

Accepted Answer

The answer of Find a linear function whose graph has...

Question 18

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 19

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 20

Find all numbers for which the rational expression is not defined.&#10;

Accepted Answer

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

Question 21

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 22

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 23

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 24

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 25

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 26

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 27

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 28

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 29

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 30

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 31

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 32

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 33

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 34

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 35

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 36

Multiply. Do not simplify.&#10;

Accepted Answer

The answer of Multiply. Do not simplify.&#10; ...

Question 37

Multiply and, if possible, simplify.&#10;

Accepted Answer

The answer of Multiply and, if possible, simplify.&#10; ...

Question 38

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 39

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 40

Simplify.&#10;

Accepted Answer

The answer of Simplify.&#10; ...

Question 41

Add, first finding the LCD. Simplify, if possible.&#10;

Accepted Answer

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

Question 42

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 43

Find the LCM.&#10;

Accepted Answer

The answer of Find the LCM.&#10; ...

Question 44

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 45

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 46

Divide and simplify.&#10;54, 12&#10;A)54&#10;B)18&#10;C)36&#10;D)108

Accepted Answer

The answer of Divide and simplify.&#10;54, 12&#10;A)54&#10;B)18&#10;C)36&#10;D)108...

Question 47

Divide and simplify.&#10;90, 18, 45&#10;A)90&#10;B)135&#10;C)54&#10;D)270

Accepted Answer

The answer of Divide and simplify.&#10;90, 18, 45&#10;A)90&#10;B)135&#10;C)54&#10;D)270...

Question 48

Find the LCM.&#10;

Accepted Answer

The answer of Find the LCM.&#10; ...

Question 49

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 50

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 51

Find the LCM.&#10;

Accepted Answer

The answer of Find the LCM.&#10; ...

Question 52

Divide and simplify.&#10;

Accepted Answer

The answer of Divide and simplify.&#10; ...

Question 53

Add, first finding the LCD. Simplify, if possible.&#10;

Accepted Answer

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

Question 54

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 55

Add, first finding the LCD. Simplify, if possible.&#10;

Accepted Answer

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

Question 56

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 57

Divide and simplify.&#10;20, 6, 30&#10;A)20&#10;B)12&#10;C)30&#10;D)60

Accepted Answer

The answer of Divide and simplify.&#10;20, 6, 30&#10;A)20&#10;B)12&#10;C)30&#10;D)60...

Question 58

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 59

Find the LCM.&#10;500, 300, 150&#10;A)1500&#10;B)500&#10;C)750&#10;D)300

Accepted Answer

The answer of Find the LCM.&#10;500, 300, 150&#10;A)1500&#10;B)500&#10;C)750&#10;D)300...

Question 60

Find the reciprocal.&#10;

Accepted Answer

The answer of Find the reciprocal.&#10; ...

Question 61

Add, first finding the LCD. Simplify, if possible.&#10;

Accepted Answer

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

Question 62

Add, first finding the LCD. Simplify, if possible.&#10;

Accepted Answer

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

Question 63

Find the LCM.&#10;

Accepted Answer

The answer of Find the LCM.&#10; ...

Question 64

Find the LCM.&#10;

Accepted Answer

The answer of Find the LCM.&#10; ...

Deck 6: Rational Expressions and Equations