Use Direct and Inverse Variation Quiz
The question sheet
Reveal any answer as you study-
A rational expression has the form p/q where p and q are polynomials and q is:
- Always negative
- Not equal to zero
- A constant
- Equal to zero
Reveal answer
Answer: Not equal to zero
Source evidence
PDF page 912: A rational expression is an expression of the form , where p and q are polynomials and q ≠ 0. q(x)
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Why must certain values of the variable be excluded from a rational expression?
- They make the numerator zero
- They make the fraction negative
- They simplify the expression
- They make the denominator zero
Reveal answer
Answer: They make the denominator zero
Source evidence
PDF page 912: When we work with a numerical fraction, it is easy to avoid dividing by zero, because we can see the number in the denominator. In order to avoid dividing by zero in a rational expression, we must not allow values of the variable that will make the denominator be zero. If the denominator is zero, the rational expression is undefined. The numerator of a rational expression may be 0—but not the denominator. So before we begin any operation with a rational expression, we examine it first to find the values that would make the denominator zero. That way, when we solve a rational equation for example, we will know whether the algebraic solutions we find are allowed or not.
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According to the source, division by zero is:
- Equal to one
- Equal to zero
- Undefined
- Equal to the numerator
Reveal answer
Answer: Undefined
Source evidence
PDF page 912: Remember, division by 0 is undefined. Here are some examples of rational expressions: 2
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What is Step 1 in determining values for which a rational expression is undefined?
- Factor the numerator
- Simplify the expression
- Set the denominator equal to zero
- Set the numerator equal to zero
Reveal answer
Answer: Set the denominator equal to zero
Source evidence
PDF page 912: Step 1. Set the denominator equal to zero. Step 2. Solve the equation in the set of reals, if possible.
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After setting the denominator equal to zero, the next step is to:
- Set the numerator to zero
- Multiply both sides
- Solve the equation in the reals
- Graph the expression
Reveal answer
Answer: Solve the equation in the reals
Source evidence
PDF page 912: Step 1. Set the denominator equal to zero. Step 2. Solve the equation in the set of reals, if possible.
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To evaluate a rational expression, you substitute values and then:
- Simplify the result
- Add the terms
- Set it equal to zero
- Factor the result
Reveal answer
Answer: Simplify the result
Source evidence
PDF page 913: To evaluate a rational expression, we substitute values of the variables into the expression and simplify, just as we have for many other expressions in this book.
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A rational expression is considered simplified when it has no common factors other than:
- The denominator
- The variable
- Zero
- One
Reveal answer
Answer: One
Source evidence
PDF page 917: Just like a fraction is considered simplified if there are no common factors, other than 1, in its numerator and denominator, a rational expression is simplified if it has no common factors, other than 1, in its numerator and denominator.
PDF page 917: A rational expression is considered simplified if there are no common factors in its numerator and denominator. For example:
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Which property is used to simplify rational expressions?
- Zero Product Property
- Equivalent Fractions Property
- Square Root Property
- Distributive Property
Reveal answer
Answer: Equivalent Fractions Property
Source evidence
PDF page 917: We use the Equivalent Fractions Property to simplify numerical fractions. We restate it here as we will also use it to simplify rational expressions.
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What is Step 1 in simplifying a rational expression?
- Evaluate for a value
- Factor numerator and denominator
- Divide out common factors
- Set denominator to zero
Reveal answer
Answer: Factor numerator and denominator
Source evidence
PDF page 919: Step 1. Factor the numerator and denominator completely. Step 2. Simplify by dividing out common factors.
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When simplifying a rational expression, you may remove common factors from a:
- Sum
- Product
- Term
- Difference
Reveal answer
Answer: Product
Source evidence
PDF page 918: To simplify rational expressions we first write the numerator and denominator in factored form. Then we remove the common factors using the Equivalent Fractions Property. Be very careful as you remove common factors. Factors are multiplied to make a product. You can remove a factor from a product. You cannot remove a term from a sum.
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According to the source, you cannot remove from a rational expression a:
- Factor
- Term from a sum
- Product
- Common factor
Reveal answer
Answer: Term from a sum
Source evidence
PDF page 918: To simplify rational expressions we first write the numerator and denominator in factored form. Then we remove the common factors using the Equivalent Fractions Property. Be very careful as you remove common factors. Factors are multiplied to make a product. You can remove a factor from a product. You cannot remove a term from a sum.
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An expression and its opposite divide to:
- The variable
- 0
- −1
- 1
Reveal answer
Answer: −1
Source evidence
PDF page 923: The opposite of a − b is b − a . a − b = −1 a ≠ b b − a An expression and its opposite divide to −1 .
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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