Rational Expressions and Equations

This video tutorial explains the process of finding the partial fraction decomposition of a rational expression. It begins with an introduction to the concept, highlighting the importance of comparing the degrees of the numerator and denominator. The tutorial then guides through setting up the partial fractions, clearing fractions using the least common denominator, and solving for unknown constants A, B, and C using specific values of X. Finally, it demonstrates how to substitute these values back into the fractions to complete the decomposition.

What is the degree of the numerator in the given rational expression?

• Degree 4

• Degree 2

• Degree 1

• Degree 3

Which type of factor is present in the denominator of the rational expression?

• Two quadratic

• Only linear

• Only quadratic

• One linear and one quadratic

What is the form of the numerator for a linear factor in partial fraction decomposition?

• A cubic expression

• A linear expression

• A quadratic expression

• A constant

What operation is performed to clear the fractions in the equation?

• Addition

• Subtraction

• Multiplication

• Division

What is the least common denominator used to clear the fractions?

• X - 2

• X - 2 and X^2 - X + 1

• X^2 - X + 1

• X + 2

Which value of x is used first to simplify the equation and solve for A?

• x = 0

• x = 1

• x = 2

• x = -1

What is the value of A after solving the equation?

• 1

• 3

• 4

• 2

What is the value of C after solving the equation?

• 2

• -1

• 0

• 1

Which value of x is used to solve for B?

• x = 0

• x = 1

• x = 2

• x = -1

What is the final form of the numerator for the quadratic factor in the decomposition?

• 3x - 1

• 3x + 1

• 2x - 1

• 2x + 1