Rational Equations and Expressions

The video tutorial covers solving rational equations, focusing on finding the least common denominator (LCD) and solving equations with restrictions. It includes examples demonstrating how to handle extraneous solutions and solve quadratic rational equations. The tutorial emphasizes the importance of identifying restrictions where the denominator equals zero and provides step-by-step solutions for various types of rational equations.

What is the first step in solving rational equations?

• Multiply all terms by the numerator

• Set the equation equal to zero

• Combine like terms

• Find the least common denominator

Why do we multiply all terms by the least common denominator?

• To combine like terms

• To simplify the numerators

• To find the restrictions

• To eliminate the denominators

In Example 2a, what is the least common denominator for the given rational expressions?

• x + 1

• x

• x times x + 1

• 1

What are the restrictions for the equation in Example 2a?

• x cannot equal 1 or -1

• x cannot equal 0 or 1

• x cannot equal 2 or -2

• x cannot equal 0 or -1

In Example 2b, what is the least common denominator for the fractions?

• 4

• x + 1

• x

• 8

What is the solution to the equation in Example 2b?

• x = -7/2

• x = 2/7

• x = -2/7

• x = 7/2

In Example 2c, what is the least common denominator for the given rational expressions?

• x times x + 3

• x

• 3

• x + 3

What is the solution to the equation in Example 2c?

• x = 3

• x = -3

• x = 0

• No solution

In Example 2d, what is the least common denominator for the given rational expressions?

• x - 1

• x

• x times x - 1

• 1

What is the solution to the equation in Example 2d?

• x = -1

• x = 3

• x = 1

• x = -3