Rational Equations and Expressions

This video tutorial teaches how to solve rational equations by eliminating denominators and checking for extraneous solutions. It explains rational expressions, demonstrates solving quadratic equations using factors, and highlights the issues with dividing by zero. The tutorial also covers using common denominators to solve rational equations and provides examples to illustrate these concepts.

What happens when you divide a number by zero?

• The result is zero.

• The result is infinity.

• The result is undefined.

• The result is the number itself.

What is a rational expression?

• A ratio of two polynomial expressions.

• A single polynomial expression.

• A ratio of two integers.

• A ratio of two rational numbers.

What must be true for a product of factors to equal zero?

• All factors must be zero.

• At least one factor must be zero.

• None of the factors can be zero.

• The product must be a positive number.

What is an extraneous solution?

• A solution that does not satisfy the original equation.

• A solution that satisfies the original equation.

• A solution that is always zero.

• A solution that is always positive.

How do you solve a rational equation?

• By subtracting the denominators.

• By dividing by the common numerator.

• By adding the numerators.

• By multiplying by the common denominator.

What is the result of multiplying and dividing by the same term?

• The result is zero.

• The result is the term itself.

• The result is undefined.

• The result is one.

What is the least common denominator used for?

• To solve rational equations.

• To subtract fractions.

• To add fractions.

• To multiply fractions.

What is the solution to the final rational equation example?

• x = 2

• x = -3

• x = -3.75

• x = 0

What should you check for after solving a rational equation?

• If the solution is negative.

• If the solution is zero.

• If the solution is positive.

• If the solution is extraneous.

What is the main goal of the lesson on rational equations?

• To learn to divide rational numbers.

• To learn to add rational numbers.

• To learn to solve rational equations by eliminating denominators.

• To learn to multiply rational numbers.