Exploring Operations with Rational Expressions: Multiply & Divide

The video tutorial covers operations with rational expressions, focusing on multiplying and dividing. It begins with a recap of basic fraction operations, then explains the process for multiplying and dividing rational expressions, including factoring and simplifying. Several examples are provided to illustrate these concepts, demonstrating how to factor expressions, apply the keep-change-flip method for division, and simplify results.

What is the result of multiplying 1/2 by 3/4?

• 2/3

• 3/8

• 1/8

• 1/4

What is the first step in dividing fractions like 1/2 by 3/4?

• Multiply the numerators

• Flip the second fraction and multiply

• Subtract the denominators

• Add the fractions

When factoring the expression x^2 - 6x - 16, which numbers should be used?

• -6 and +1

• -8 and +2

• -4 and +4

• -2 and +8

What is the first step in simplifying the expression 2x^2 + 7x + 6?

• Apply the quadratic formula

• Guess and check for factors

• Identify the GCF

• Factor by grouping

What is the simplified form of the expression (x-8)(x+2) / (x-8)(x-8) after canceling common factors?

• x+2

• 1 / (2x+3)

• 2x+3

• 1 / (x+2)

What is the correct factoring pattern for the expression 9x^2 - 16?

• (3x-4)^2

• (3x+4)(3x-4)

• (9x-16)(x+1)

• (3x+4)^2

What is the result of simplifying the expression (2x+3)(x+2) / (x-8)(x-8) after canceling common factors?

• 1 / (2x+3)

• 2x+3

• x+2

• 1 / (x+2)

What is the result of dividing 3x^2 - 28x + 32 by y^2 - 3y - 18 using the keep-change-flip method?

• (3x+4)(y+3) / 12(x-8)

• (3x-4)(y+3) / 12(x-8)

• (3x+4)(y-6) / 12(x-8)

• (3x-4)(y-6) / 12(x-8)

How do you simplify the expression 3y(y+6) / 15y^2?

• 3 / 5

• 1 / 5y

• y+6 / 5

• y+6 / 5y

What is the simplified form of the expression 18x^2y^3b / 12xy after cross simplification?

• 3x^2y^3b / 2

• 3y^2b / 2

• 3xy^2b / 2

• 3x^2y^2b / 2