Exploring Multiplying and Dividing Rational Expressions

In this lesson, Kirk Wier covers Unit 10, Lesson 7 of Common Core Algebra 2, focusing on multiplying and dividing rational expressions. The lesson begins with a review of multiplying numerical fractions and extends these concepts to algebraic fractions. Key techniques include factoring and cross-cancelling. The lesson progresses through exercises that involve simplifying both simple and complex rational expressions, including those already in factored form. The video also covers simplifying quotients by converting division into multiplication. The lesson concludes with a multiple-choice problem to reinforce the concepts learned.

What is the first step in multiplying two numerical fractions?

• Divide the numerators

• Subtract the denominators

• Multiply the numerators and denominators

• Add the numerators

When simplifying rational expressions, what should you do after factoring?

• Divide the factors

• Cancel common factors

• Multiply the factors

• Add the factors

In the expression (6/8) * (10/3), what is the simplified form after factoring and canceling?

• 4/5

• 5/4

• 3/2

• 5/2

What is the result of simplifying the expression (8y^4)/(3x) * (10x^2)/(5y^3)?

• 8y / 3x^2

• 8y^4 / 3x

• 8y / 3x

• 8y^7 / 15x^3

What is the simplified form of (2x(x+6))/(4(x+2)) * ((x-6)(x+2))/((x-6)(x+6))?

• x / 2

• 2x / 4

• x / 4

• 2x / 2

What is the simplified form of (3x+1)(3x-1)/(2x^2(x-3)) * (4x(x-1))/((x+3)(x-1))?

• -2 / x

• -2 / x^2

• 2 / x

• 2 / x^2

What is the first step in simplifying a quotient of rational expressions?

• Add the fractions

• Divide the numerators

• Multiply by the reciprocal of the second fraction

• Subtract the fractions

What is the simplified form of (3x^2y^5)/(15x^8y^7) ÷ (2y^2)/(10x^2)?

• 6y^2 / 2x^6

• y^2 / x^6

• y^2 / 2x^6

• 6y^2 / x^6

What is the simplified form of (x^2-25)/(3x) ÷ (x+5)/(9x)?

• 3(x+5)

• 3(x-5)

• 3(x+5)/(x-5)

• 3(x-5)/(x+5)

What is the simplified form of (2x^2-8x)/(4x) ÷ (x-2)/(2x)?

• x

• 2x

• x-2

• 2(x-2)