Questions and Answers
In what form is a Rational Algebraic Expression?
Fraction Form (n/d)
The denominator is not equal to zero.
True
What is a Rational Algebraic Equation?
Equations that contain one or more Rational Expressions
Simplify this Rational Algebraic Expression: 16p^2 / 28p
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Simplify this Rational Algebraic Expression: 15n/30n^3
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What is a Rational Algebraic Expression?
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Find the LCD of 2/x + 1/2.
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What type of expression are the numerator and denominator in RAE?
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Simplify x + 6/x^2 + 5x − 6.
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What is a Rational Algebraic Equation?
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Find the LCD of 3x and 2x.
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These are equations that contain one or more Rational Algebraic Expressions.
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Simplify: 2r − 4/r − 2.
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Refers to the equality of Rational Expressions.
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Find the LCD of 2x and 2x.
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What is the sum of a number and 10?
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What is 6 more than a number?
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What does '17 added to a number yields to 3' represent?
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What is the quotient of a number and 9?
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What is one-halves of a number to 14?
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What does 'Twenty-five times a number' represent?
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What is the ratio of a number to 16?
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What does '3 less a number amounts to 10' mean?
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What is twenty-six added to a number?
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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 ).
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