Final answer:
To find the partial fraction decomposition of (x²-4x+6) / (x−3)³, factor the denominator and express the given fraction as the sum of its partial fraction components: A/(x − 3), B/(x − 3)², and C/(x − 3)³. Solve for the values of A, B, and C using the common denominator method.
Step-by-step explanation:
To perform the partial fraction decomposition of (x²-4x+6) / (x−3)³, we first factor the denominator (x − 3)³ as (x − 3)(x − 3)(x − 3). Then, we express the given fraction as the sum of its partial fraction components:
- First component: A/(x − 3)
- Second component: B/(x − 3)²
- Third component: C/(x − 3)³
We can then solve for the values of A, B, and C by performing the common denominator method and comparing the numerator coefficients.
Let me know if you need help solving for A, B, and C or if you have any other questions!