Question 1

Find the domain of the rational expression.&#10;

Accepted Answer

The domain of a rational expression excludes values that make the denominator zero. In this case, the denominator is $0$ when $x = -7$, so the domain is all real numbers except $x = -7$.

Question 2

Simplify the expression.&#10;

Accepted Answer

The expression can be simplified by factoring out a -2 from the numerator, resulting in $\frac{-2(x+y)}{x+y}$. The $(x+y)$ terms cancel out, leaving $-2$.

Question 3

Find the domain of the rational expression.&#10;

Accepted Answer

The denominator of the rational expression $5x + 2$ cannot be zero because division by zero is undefined. Solving $5x + 2 = 0$ for $x$ gives $x = -\frac{2}{5}$. Therefore, the domain excludes $-\frac{2}{5}$, making option B correct.

Question 4

Find the domain of the rational expression.&#10;

Accepted Answer

The domain of a rational expression excludes values that make the denominator zero. Since the denominator is $4y$, the only value that needs to be excluded from the domain is $y = 0$, making option A correct.

Question 5

Find the domain of the rational expression.&#10;

Accepted Answer

The answer of Find the domain of the rational expression.&#10;...

Question 6

Simplify the expression.&#10;

Accepted Answer

The expression simplifies to -1 because the numerator and denominator are negatives of each other, so dividing them gives -1.

Question 7

Find the domain of the rational expression.&#10;

Accepted Answer

The domain of a rational expression excludes values that make the denominator zero. For $f(x) = \frac{x}{3x - 5}$, the denominator is zero when $3x - 5 = 0$, solving for $x$ gives $x = \frac{5}{3}$. Therefore, the domain is all real numbers except $x = \frac{5}{3}$.

Question 8

Find the domain of the rational expression.&#10;

Accepted Answer

The domain of a rational expression excludes values that make the denominator zero. Factoring the denominator $x^2 - 4x - 60 = (x - 10)(x + 6)$, we find that $x \neq 10$ and $x \neq -6$ to avoid division by zero. The numerator does not affect the domain, so choices involving $\frac{1}{8}$ or $0$ are incorrect.

Question 9

Find the domain of the rational expression.&#10;

Accepted Answer

The domain of a rational expression excludes values that make the denominator equal to zero. For $f(x) = \frac{36x^2 - 81}{7x - 35}$, the denominator is $7x - 35$. Setting the denominator equal to zero gives $7x - 35 = 0$, which simplifies to $x = 5$. Therefore, the domain is all real numbers except $x = 5$.

Question 10

Find the domain of the rational expression.&#10;

Accepted Answer

The denominator does not contain the variable $x$, so there are no restrictions on $x$. The domain includes all real numbers.

Question 11

Simplify the expression.&#10;

Accepted Answer

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

Question 12

Simplify the expression.&#10;

Accepted Answer

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

Question 13

Find the domain of the rational expression.&#10;

Accepted Answer

The answer of Find the domain of the rational expression.&#10;...

Question 14

Find the domain of the rational expression.&#10;

Accepted Answer

The answer of Find the domain of the rational expression.&#10;...

Question 15

Simplify the expression.&#10;

Accepted Answer

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

Question 16

Simplify the expression.&#10;

Accepted Answer

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

Question 17

Find the domain of the rational expression.&#10;

Accepted Answer

The answer of Find the domain of the rational expression.&#10;...

Question 18

Simplify the expression.&#10;

Accepted Answer

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

Question 19

Find the domain of the rational expression.&#10;

Accepted Answer

The answer of Find the domain of the rational expression.&#10;...

Question 20

Find the domain of the rational expression.&#10;

Accepted Answer

The answer of Find the domain of the rational expression.&#10;...

Question 21

Simplify the expression.&#10;

Accepted Answer

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

Question 22

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 23

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 24

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 25

Simplify the expression.&#10;

Accepted Answer

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

Question 26

List four equivalent forms for the rational expression.&#10;

Accepted Answer

The answer of List four equivalent forms for the rational...

Question 27

List four equivalent forms for the rational expression.&#10;

Accepted Answer

The answer of List four equivalent forms for the rational...

Question 28

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 29

Simplify the expression.&#10;

Accepted Answer

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

Question 30

Simplify the expression.&#10;

Accepted Answer

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

Question 31

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 32

Simplify the expression.&#10;

Accepted Answer

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

Question 33

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 34

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 35

Simplify the expression.&#10;

Accepted Answer

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

Question 36

Simplify the expression.&#10;

Accepted Answer

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

Question 37

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 38

Simplify the expression.&#10;

Accepted Answer

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

Question 39

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 40

Simplify the expression.&#10;

Accepted Answer

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

Question 41

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 42

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 43

Solve the problem.&#10;

Accepted Answer

The answer of Solve the problem.&#10; ...

Question 44

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 45

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 46

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 47

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 48

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 49

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 50

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 51

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 52

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 53

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 54

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 55

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 56

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 57

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 58

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 59

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 60

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 61

Find the product and simplify.&#10;

Accepted Answer

The answer of Find the product and simplify.&#10; ...

Question 62

Find the quotient and simplify.&#10;

Accepted Answer

The answer of Find the quotient and simplify.&#10; ...

Question 63

Find the quotient and simplify.&#10;

Accepted Answer

The answer of Find the quotient and simplify.&#10; ...

Question 64

Find the quotient and simplify.&#10;

Accepted Answer

The answer of Find the quotient and simplify.&#10; ...

Deck 7: Rational Expressions