Podcast
Questions and Answers
What is a rational equation?
What is a rational equation?
What is the first step in solving rational equations?
What is the first step in solving rational equations?
State the restrictions
What must be done to clear an equation of fractions?
What must be done to clear an equation of fractions?
Multiply both sides by the LCD of all rational expressions
When solving a rational equation, you should not check the proposed solutions against the restrictions on the variable.
When solving a rational equation, you should not check the proposed solutions against the restrictions on the variable.
Signup and view all the answers
What is the method to solve a rational equation?
What is the method to solve a rational equation?
Signup and view all the answers
What do you use when adding or subtracting rational equations?
What do you use when adding or subtracting rational equations?
Signup and view all the answers
What are you doing when you add or subtract rational equations with an equal sign?
What are you doing when you add or subtract rational equations with an equal sign?
Signup and view all the answers
Study Notes
Rational Equations
- A rational equation features one or more fractional terms.
- The primary goal when solving is to eliminate the denominators within the equation.
Steps for Solving Rational Equations
- Begin by establishing any restrictions on the variable, determining values that would make the denominator zero.
- Multiply both sides of the equation by the Least Common Denominator (LCD) of all rational expressions to eliminate fractions.
- Solve the simplified equation that results after clearing the denominators.
- Check all proposed solutions against the restrictions to ensure validity, rejecting any that violate these conditions.
Techniques for Solving
- When solving, focus on multiplying denominators by numerators to facilitate the cancellation of terms.
- This method simplifies the equation without introducing extraneous solutions.
Adding & Subtracting Rational Equations
- Use the Least Common Denominator (LCD) when adding or subtracting rational expressions to combine them properly.
- Ensure that the resulting expression maintains equivalent values in the context of the equations.
Solving for Variables in Rational Equations
- When presented with an equal sign during addition or subtraction of rational equations, the objective shifts to solving for the variable, such as ( x ).
- Follow the same principles of clearing fractions and establishing valid solutions.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the essential techniques for solving rational equations. Learn how to eliminate denominators, apply the Least Common Denominator (LCD), and verify solutions against restrictions. Test your understanding of adding and subtracting rational expressions.
