Rational Algebraic Expressions and Equations

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

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

What does '17 added to a number yields to 3' represent?

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-halves of a number to 14?

x/14 Signup and view all the answers

What does 'Twenty-five times a number' represent?

25x Signup and view all the answers

What is the ratio of a number to 16?

x/16 Signup and view all the answers

What does '3 less a number amounts to 10' mean?

3 - x = 10 Signup and view all the answers

What is twenty-six added to a number?

x + 26 Signup and view all the answers

What is seven less a number?

7 - x Signup and view all the answers

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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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.