Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
What is a Rational Equation?
What is a Rational Equation?
An equation with one or more rational expressions
What is the first step in the LCD method to solve rational equations?
What is the first step in the LCD method to solve rational equations?
- Multiply both sides by LCD (correct)
- Add both sides
- Factor both sides
- Cross multiply
Describe the Cross Multiplication Method.
Describe the Cross Multiplication Method.
If in the form a/b = c/d, then cross multiply and solve the result.
What are Domain Restrictions?
What are Domain Restrictions?
Signup and view all the answers
What does the Zero Product Property state?
What does the Zero Product Property state?
Signup and view all the answers
What is an Extraneous Solution?
What is an Extraneous Solution?
Signup and view all the answers
Does multiplication need a common denominator?
Does multiplication need a common denominator?
Signup and view all the answers
Flashcards are hidden until you start studying
Study Notes
Rational Equations
- Defined as equations that include one or more rational expressions.
LCD Method
- Involves multiplying both sides of the equation by the Least Common Denominator (LCD).
- Simplifies the equation to help solve it.
- Applicable to any rational equation.
Cross Multiplication Method
- Used when the equation is in the form a/b = c/d.
- Involves cross-multiplying the terms, leading to the equation ad = bc.
- Based on the property of proportional ratios.
Domain Restrictions
- Identify numbers that are not valid solutions in the context of the equation.
- Determined through the application of the zero product property.
Zero Product Property
- States that if the product of two numbers (a and b) equals zero (ab = 0), at least one of those numbers must be zero (a = 0 or b = 0).
- This principle is essential in solving equations involving products.
Extraneous Solutions
- Refers to solutions obtained that do not satisfy the original equation.
- Often arise from operations performed during solving, such as multiplying or squaring both sides.
Common Denominator in Multiplication
- No requirement exists for multiplication of rational expressions to have a common denominator.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
