Simplifying Rational Expressions and Factors

The video tutorial explains how to handle rational expressions, focusing on finding their domain and simplifying them. It covers the importance of avoiding zero in the denominator, using factoring techniques, and applying the diamond method for simplification. The tutorial also discusses alternative methods and concludes with a summary of the process.

What is a rational expression?

• An inequality

• An equation with an equal sign

• An expression without an equal sign

• A polynomial equation

Why is it important to find the domain of a rational expression?

• To avoid division by zero

• To determine the range of the expression

• To identify the zeros of the numerator

• To simplify the expression

What should be done first when simplifying a rational expression?

• Find the zeros of the numerator

• Factor the numerator

• Rearrange the terms to have x squared in front

• Cancel common factors

What happens if you plug in a value that makes the denominator zero?

• The expression equals zero

• The expression becomes negative

• The expression becomes undefined

• The expression equals one

What should be factored out to simplify the expression further?

• A negative one

• A positive one

• A constant term

• An x squared term

Which values of x make the denominator zero in the given expression?

• x = 0 and x = 5

• x = 0 and x = -5

• x = 1 and x = -1

• x = -5 and x = 5

What is the purpose of the diamond method in simplifying the numerator?

• To rearrange the terms

• To cancel common factors

• To factor the numerator

• To find the zeros of the numerator

What two numbers multiply to -25 and add to 0?

• 10 and -2.5

• 25 and -1

• 5 and -5

• 15 and -10

What happens when you cancel common factors in a fraction?

• The fraction equals zero

• The fraction becomes undefined

• The fraction simplifies

• The fraction equals one

How does Khan Academy prefer to handle negative signs in rational expressions?

• Move them to the numerator

• Ignore them

• Cancel them out

• Leave them in the denominator