Rational Algebraic Expressions Flashcards

Questions and Answers

In what form is Rational Algebraic Expression?

Fraction Form (n/d)

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

4p/7 Signup and view all the answers

Simplify this Rational Algebraic Expression: 15n/30n^3

1/2n^2 Signup and view all the answers

What is a Rational Algebraic Expression?

an expression that can be written as a ratio of two polynomials Signup and view all the answers

Find the LCD of 2/x + 1/2.

2x Signup and view all the answers

What type of expression are the numerator and denominator in RAE?

Polynomials Signup and view all the answers

Simplify: x + 6/x^2 + 5x − 6.

1/x-1 Signup and view all the answers

What is a Rational Algebraic Equation?

An algebraic expression which can be represented as a quotient of two polynomials. Signup and view all the answers

Find the LCD of 3x and 2x.

6x Signup and view all the answers

These are equations that contain one or more Rational Algebraic Expressions.

Rational Algebraic Equation Signup and view all the answers

Simplify: 2r − 4/r − 2.

2 Signup and view all the answers

Refers to the equality of Rational Expressions.

Rational Algebraic Equation Signup and view all the answers

Find the LCD of 2x and 2x.

4x Signup and view all the answers

What is the sum of a number and 10?

x + 10 Signup and view all the answers

What is 6 more than a number?

x + 6 Signup and view all the answers

17 added to a number yields to 3.

x + 17 = 3 Signup and view all the answers

What is the quotient of a number and 9?

x/9 Signup and view all the answers

What is one-half of a number to 14?

x/14 Signup and view all the answers

Twenty-five times a number?

25x Signup and view all the answers

What is the ratio of a number to 16?

x/16 Signup and view all the answers

3 less a number amounts to 10.

3 - x = 10 Signup and view all the answers

Twenty-six added to a number.

x + 26 Signup and view all the answers

Seven less a number.

7 - x Signup and view all the answers

Study Notes

Rational Algebraic Expressions

Formed as a fraction of two polynomials (n/d).
Must have a non-zero denominator to be valid.

Rational Algebraic Equations

Contain one or more rational expressions.
Represent an equality involving rational expressions.

Simplification of Rational Expressions

Example: 16p² / 28p simplifies to 4p / 7.
Example: 15n / 30n³ simplifies to 1 / 2n².
Example: Simplifying (x + 6) / (x² + 5x - 6) results in 1 / (x - 1).
Example: (2r - 4) / (r - 2) simplifies to 2.

Finding Least Common Denominator (LCD)

LCD of 2/x + 1/2 is 2x.
LCD of 3x and 2x is 6x.
LCD of 2x and 2x is 4x.

Characteristics of Rational Expressions

Both the numerator and denominator must be polynomials.
They are expressed as a ratio of two polynomial functions.

Simple Algebraic Terms

x + 10 represents the sum of a number and 10.
x + 6 indicates six more than a number.
x + 17 = 3 describes adding 17 to a number resulting in 3.
x/9 denotes the quotient of a number and 9.
x/14 signifies one-half of a number.
25x is the representation of twenty-five times a number.
x/16 shows the ratio of a number to 16.
3 - x = 10 conveys that three less a number equals ten.
x + 26 indicates twenty-six added to a number.
7 - x represents seven less a number.

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Description

Test your knowledge of Rational Algebraic Expressions and Equations with these flashcards. Each card presents a term or concept followed by its definition, covering essential properties and simplification techniques. Perfect for students looking to reinforce their understanding of rational algebra.