Questions and Answers
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?
Describe the Cross Multiplication Method.
If in the form a/b = c/d, then cross multiply and solve the result.
What are Domain Restrictions?
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What does the Zero Product Property state?
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What is an Extraneous Solution?
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Does multiplication need a common denominator?
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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.
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Description
This quiz covers key concepts regarding rational equations, including definitions and solving methods such as the LCD and cross multiplication. Ideal for students looking to reinforce their understanding of these essential algebraic concepts.
