Question

First see if you can cancel factors in the numerator and denominator. Then, using factors from the denominator make an equation stating that the fraction = A/(repeatedfactor) + B/(repeatedfactor²) + C/(otherfactor). where A, B and C are constants. Multiply both sides by the denominator to give the numerator = A(repeated factor) + B(otherfactor) + c(repeatedfactor²), then by substituting x = 0, we can evauate B. Then by evaluating x as 'root of otherfactor', solve for C and then equate the coefficients of x² for the value of A (often A = 0)

What is the technique for solving a fraction using partial fraction decomposition?
A) Canceling factors in the numerator and denominator
B) Multiplying both sides by the denominator
C) Substituting x = 0
D) Equating coefficients of x²

Answer 1

The technique for solving a fraction using partial fraction decomposition involves several steps: canceling factors, making an equation, multiplying by the denominator, substituting values, and equating coefficients of x².

Step-by-step explanation:

The technique for solving a fraction using partial fraction decomposition involves several steps:

1. First, see if you can cancel factors in the numerator and denominator.
2. Using factors from the denominator, make an equation stating that the fraction is equal to A/(repeated factor) + B/(repeated factor²) + C/(other factor), where A, B, and C are constants.
3. Multiply both sides of the equation by the denominator to give the numerator = A(repeated factor) + B(other factor) + C(repeated factor²).
4. Substitute x = 0 to evaluate B.
5. Evaluate x as the root of the other factor to solve for C.
6. Equate the coefficients of x² to find the value of A.