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Questions and Answers
In what form is a Rational Algebraic Expression?
In what form is a Rational Algebraic Expression?
Fraction Form (n/d)
The denominator is not equal to zero.
The denominator is not equal to zero.
True
What is a Rational Algebraic Equation?
What is a Rational Algebraic Equation?
Equations that contain one or more Rational Expressions
Simplify this Rational Algebraic Expression: 16p^2 / 28p
Simplify this Rational Algebraic Expression: 16p^2 / 28p
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Simplify this Rational Algebraic Expression: 15n/30n^3
Simplify this Rational Algebraic Expression: 15n/30n^3
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What is a Rational Algebraic Expression?
What is a Rational Algebraic Expression?
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Find the LCD of 2/x + 1/2.
Find the LCD of 2/x + 1/2.
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What type of expression are the numerator and denominator in RAE?
What type of expression are the numerator and denominator in RAE?
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Simplify x + 6/x^2 + 5x − 6.
Simplify x + 6/x^2 + 5x − 6.
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What is a Rational Algebraic Equation?
What is a Rational Algebraic Equation?
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Find the LCD of 3x and 2x.
Find the LCD of 3x and 2x.
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These are equations that contain one or more Rational Algebraic Expressions.
These are equations that contain one or more Rational Algebraic Expressions.
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Simplify: 2r − 4/r − 2.
Simplify: 2r − 4/r − 2.
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Refers to the equality of Rational Expressions.
Refers to the equality of Rational Expressions.
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Find the LCD of 2x and 2x.
Find the LCD of 2x and 2x.
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What is the sum of a number and 10?
What is the sum of a number and 10?
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What is 6 more than a number?
What is 6 more than a number?
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What does '17 added to a number yields to 3' represent?
What does '17 added to a number yields to 3' represent?
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What is the quotient of a number and 9?
What is the quotient of a number and 9?
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What is one-halves of a number to 14?
What is one-halves of a number to 14?
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What does 'Twenty-five times a number' represent?
What does 'Twenty-five times a number' represent?
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What is the ratio of a number to 16?
What is the ratio of a number to 16?
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What does '3 less a number amounts to 10' mean?
What does '3 less a number amounts to 10' mean?
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What is twenty-six added to a number?
What is twenty-six added to a number?
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What is seven less a number?
What is seven less a number?
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Study Notes
Rational Algebraic Expressions
- Rational algebraic expressions are written in fraction form, represented as ( \frac{n}{d} ), where ( n ) and ( d ) are polynomials.
- The denominator of a rational expression must not equal zero to be defined.
Rational Algebraic Equations
- Rational algebraic equations comprise one or more rational expressions in their structure.
- An algebraic expression can be expressed as a quotient of two polynomials, making it a rational algebraic equation.
Simplification of Expressions
- Simplifying ( \frac{16p^2}{28p} ) results in ( \frac{4p}{7} ).
- Simplifying ( \frac{15n}{30n^3} ) yields ( \frac{1}{2n^2} ).
- Simplification of ( \frac{x + 6}{x^2 + 5x - 6} ) simplifies to ( \frac{1}{x - 1} ).
- Simplifying ( \frac{2r - 4}{r - 2} ) leads to the result of 2.
Finding the Least Common Denominator (LCD)
- The LCD of ( \frac{2}{x} + \frac{1}{2} ) is ( 2x ).
- The LCD of ( 3x ) and ( 2x ) is ( 6x ).
- The LCD of ( 2x ) and ( 2x ) is ( 4x ).
Polynomials in Rational Expressions
- Both the numerator and denominator in rational algebraic equations consist of polynomials.
Translating Word Expressions to Algebraic Forms
- The sum of a number and 10 is represented as ( x + 10 ).
- Six more than a number is expressed as ( x + 6 ).
- The equation for 17 added to a number yielding 3 is ( x + 17 = 3 ).
- The quotient of a number and 9 is represented as ( \frac{x}{9} ).
- One-half of a number leading to 14 is expressed as ( \frac{x}{14} ).
- Twenty-five times a number is shown as ( 25x ).
- The ratio of a number to 16 is ( \frac{x}{16} ).
- An expression stating that 3 less a number amounts to 10 is ( 3 - x = 10 ).
- Twenty-six added to a number is expressed as ( x + 26 ).
- Seven less a number is represented as ( 7 - x ).
Studying That Suits You
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Description
Test your understanding of rational algebraic expressions and equations with these flashcards. Each card covers essential concepts such as their definitions, forms, and simplification techniques. Perfect for students looking to master this topic in algebra.
