Find the Partial Fraction Decomposition for the Given Rational Expression

question 64

Multiple Choice

Find the partial fraction decomposition for the given rational expression. Use the technique of Gaussian
elimination to find A, B, and C.
- $$\frac { - 3 x ^ { 2 } + 7 x - 10 } { ( x + 2 ) ( x - 1 ) ^ { 2 } } = \frac { A } { x + 2 } + \frac { B } { x - 1 } - \frac { C } { ( x - 1 ) ^ { 2 } }$$

• A) \(\frac { - 4 } { x + 2 } + \frac { 1 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }\)
• B) \(\frac { - 4 } { x + 2 } + \frac { 2 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }\)
• C) \(\frac { 4 } { x + 2 } + \frac { 1 } { x - 1 } - \frac { 2 } { ( x - 1 ) ^ { 2 } }\)
• D) \(\frac { - 4 } { x + 2 } + \frac { 1 } { x - 1 } + \frac { 2 } { ( x - 1 ) ^ { 2 } }\)

---

Definitions:

Cost

The amount of money that needs to be spent to purchase, produce, or maintain something.

Benefit

An advantage or profit gained from something, often referring to employment perks beyond salary, such as health insurance.

Factory Overhead Cost

Expenses associated with operating a factory that can't be directly linked to a specific product, including costs like utilities and maintenance.

Conversion Cost

The combined cost of direct labor and manufacturing overheads required to convert raw materials into finished products.