Rational Expressions and Factoring

The video tutorial explains how to simplify rational expressions by factoring both the numerator and the denominator. It covers two examples, detailing the process of identifying the greatest common factor, factoring trinomials into binomials, and recognizing excluded values to avoid division by zero. The tutorial concludes with the simplification of the expressions, ensuring a clear understanding of the process.

What is the first step in simplifying a rational expression?

• Multiply the numerator and denominator

• Subtract the numerator from the denominator

• Factor the numerator and denominator

• Add the numerator and denominator

What is the greatest common factor of 7x and 63?

• 1

• 9

• 7

• 63

Which of the following is a factor of the expression x^2 - x - 6?

• x + 3

• x - 3

• x + 6

• x - 2

What is the simplified form of the expression (x + 9)/(x + 9)?

• 0

• x + 9

• 1

• x

What is the greatest common factor of 2x^2 - 8?

• 4

• 2

• 8

• x

What is the simplified form of the expression (x^2 - 4)/(x^2 - x - 6)?

• (x + 3)/(x - 2)

• (x - 3)/(x + 2)

• (x + 2)/(x + 3)

• (x - 2)/(x - 3)

Which value of x makes the denominator of the expression x^2 - x - 6 equal to zero?

• x = -3

• x = -2

• x = 2

• x = 3

What is the excluded value for the expression (x + 2)/(x - 3)?

• x = -2

• x = -3

• x = 3

• x = 2

What is the result of simplifying (x + 2)/(x + 2)?

• 1

• x + 2

• 0

• x

What is the factorization of x^2 - 4?

• (x + 4)(x - 4)

• (x + 3)(x - 3)

• (x + 1)(x - 1)

• (x + 2)(x - 2)