Simplifying Rational Expressions

The video tutorial explains how to find the quotients of given functions G(x) and H(x) divided by F(x). It provides a detailed step-by-step process for simplifying these expressions by dividing each term in the numerator by the monomial in the denominator. The tutorial emphasizes the importance of simplifying fractions and maintaining positive exponents.

What are the functions given in the problem statement?

• F(x), G(x), and H(x)

• X(x), Y(x), and Z(x)

• A(x), B(x), and C(x)

• P(x), Q(x), and R(x)

What is the expression for G(x) divided by F(x)?

• 6x^3 + 2 divided by 12x^4

• 6x^4 + 2 divided by 12x^3

• 12x^3 + 2 divided by 6x^4

• 12x^4 + 2 divided by 6x^3

How do you simplify 12x^4 divided by 6x^3?

• 2x

• 2x^2

• x

• x^2

What is the simplified form of 2 divided by 6x^3?

• 1/2x^2

• 1/2x^3

• 1/3x^3

• 1/3x^2

What is the expression for H(x) divided by F(x)?

• 36x^9 + 24x^6 + 2 divided by 6x^3

• 36x^6 + 24x^9 + 2 divided by 6x^3

• 24x^9 + 36x^6 + 2 divided by 6x^3

• 24x^6 + 36x^9 + 2 divided by 6x^3

How do you simplify 36x^9 divided by 6x^3?

• 6x^2

• 6x^9

• 6x^3

• 6x^6

What is the simplified form of 24x^6 divided by 6x^3?

• 4x^6

• 4x^3

• 4x^2

• 4x

What is the simplified form of 2 divided by 6x^3?

• 1/2x^3

• 1/3x^2

• 1/2x^2

• 1/3x^3

What is the common factor between 2 and 6 in the simplification process?

• 1

• 6

• 3

• 2

What is the final simplified form of H(x) divided by F(x)?

• 6x^3 + 4x^6 + 1/3x^3

• 6x^6 + 4x^3 + 1/3x^3

• 6x^6 + 4x^3 + 1/2x^3

• 6x^3 + 4x^6 + 1/2x^3