Algebra 2 - Rational Expressions Flashcards

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Questions and Answers

How do you add or subtract rational expressions with the same denominator?

Add or subtract the numerators and keep the denominators, then simplify your answer if possible.

What is the equation for rational expressions with a not common denominator?

a/b +/- c/d = (ad +/- cb) / bd

What is a complex rational expression and how would you simplify it? Give an example.

A complex rational expression is two different rational expressions multiplied or divided by each other. For example, (1 + 1/x) / (1 - 1/x) = (x + 1) / (x - 1).

How do you find the least common denominator (LCD) for rational expressions with denominators of x² - 100 and x² - 20x + 100?

Factoring yields (x - 10)(x + 10) for x² - 100 and (x - 10)² for x² - 20x + 100. The LCD is (x + 10)(x - 10)². Signup and view all the answers

What does 'undefined' refer to in the context of rational expressions?

When the denominator equals 0. Signup and view all the answers

What is referred to as 'domain' in rational expressions?

The values of x. Signup and view all the answers

What are the steps for simplifying rational expressions?

<ol> <li>Factor numerator and denominator. 2. List all exclusions. 3. Cancel common factors.</li> </ol> Signup and view all the answers

What are the steps for multiplying rational expressions?

<ol> <li>Factor all numerators and denominators. 2. List all the exclusions. 3. Cancel common factors diagonally or vertically. 4. Multiply across.</li> </ol> Signup and view all the answers

What are the steps for dividing a rational expression?

<ol> <li>Factor all numerators and denominators. 2. List exclusions. 3. Multiply by the reciprocal of the divisor. 4. List any additional exclusions. 5. Cancel common factors. 6. Multiply across.</li> </ol> Signup and view all the answers

How do you add and subtract rational expressions with different denominators containing no common factors?

<ol> <li>Use the property. 2. Simplify the numerator. 3. Simplify the answer, if possible.</li> </ol> Signup and view all the answers

How do you add and subtract rational expressions with different denominators containing common factors?

<ol> <li>Factor denominators. 2. Determine the LCD, which is the product of the highest power of every different factor. 3. Simplify.</li> </ol> Signup and view all the answers

What is the definition of the least common denominator (LCD)?

Product of the highest power of every different factor. Signup and view all the answers

Study Notes

Adding and Subtracting Rational Expressions

With the same denominator, add or subtract the numerators and retain the common denominator.
Always simplify the final answer if possible.

Rational Expressions with Different Denominators

The formula for addition or subtraction involves multiplying each term by the other denominator: a/b ± c/d = (ad ± cb) / bd.

Complex Rational Expressions

Defined as the division or multiplication of two different rational expressions.
Example: ((1 + \frac{1}{x}) / (1 - \frac{1}{x}) = \frac{x + 1}{x - 1}).

Finding the Least Common Denominator (LCD)

Factor the denominators; for example, (x^2 - 100) factors to ((x - 10)(x + 10)) and (x^2 - 20x + 100) factors to ((x - 10)^2).
The LCD is determined by the highest power of each factor: ((x + 10)(x - 10)^2).

Undefined Rational Expressions

An expression becomes undefined when the denominator equals zero.

Domain of Rational Expressions

The domain is composed of all permissible values of (x) that do not result in a zero denominator.

Simplifying Rational Expressions

Begin by factoring both the numerator and denominator.
Identify and list all exclusions (values that make the denominator zero).
Cancel any common factors.

Multiplying Rational Expressions

Factor all numerators and denominators first.
List exclusions to avoid division by zero.
Cancel common factors either diagonally or vertically before multiplying across.

Dividing Rational Expressions

Similar to multiplication: factor first and list exclusions.
To divide, multiply by the reciprocal of the second rational expression.
Cancel common factors and multiply across.

Adding and Subtracting Rational Expressions with Different Denominators

Follow the property of rational expressions.
Simplify the numerator first before finding the overall simplification of the answer.

Adding and Subtracting with Common Factors

Begin by factoring denominators.
Determine the LCD as the product of the highest powers of all distinct factors, then simplify.

Least Common Denominator (LCD)

Defined as the product of the highest powers of each different factor involved in the denominators of rational expressions.

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Description

Test your knowledge of rational expressions with these flashcards. Learn how to add, subtract, and simplify rational expressions, whether they have common or different denominators. This resource is perfect for mastering complex rational expressions as well.