Partial Fraction Decomposition Concepts

This video tutorial explains the process of partial fraction decomposition for rational expressions with repeated linear factors in the denominator. It begins by verifying the degree of the numerator is less than the denominator, then factors the denominator completely. The tutorial sets up the partial fractions and solves for unknown constants using specific values of X. Finally, it presents the complete partial fraction decomposition of the original rational expression.

Why is it important to verify that the degree of the numerator is less than the degree of the denominator before setting up partial fractions?

• To simplify the numerator

• To avoid unnecessary calculations

• To factor the denominator correctly

• To ensure the expression is a proper fraction

What is the first step in factoring the denominator completely?

• Simplify the numerator

• Identify repeated factors

• Factor out the greatest common factor

• Perform long division

How many fractions are set up in the partial fraction decomposition when there are three linear factors in the denominator, with one being repeated?

• Five

• Four

• Three

• Two

What method can be used to find the values of the constants A, B, and C in partial fraction decomposition?

• Simplifying the numerator

• Performing polynomial division

• Factoring the numerator

• Using specific values of X

What is the value of A when X is set to 0 in the equation?

• 12

• 3

• 6

• 9

What is the next convenient value of X to use after X = 0?

• X = -2

• X = 1

• X = -1

• X = 2

What is the value of C when X is set to -1?

• 3

• 6

• 9

• 12

After finding A and C, what value of X is used to find B?

• X = 2

• X = 1

• X = -1

• X = 0

What is the final value of B after solving the equation?

• 2

• -1

• 0

• 1

What is the partial fraction decomposition of the original rational expression?

• 5/X + 2/(X+1) + 6/(X+1)^2

• 6/X - 1/(X+1) + 9/(X+1)^2

• 4/X - 3/(X+1) + 8/(X+1)^2

• 7/X + 1/(X+1) + 5/(X+1)^2