Write the Partial Fraction Decomposition of the Rational Expression $$\frac { - 3 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$

question 38

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { - 3 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$

• A) \(\frac { 2 } { x + 2 } + \frac { 5 } { x + 1 } + \frac { - 2 } { ( x + 1 ) ^ { 2 } }\)
• B) \(\frac { - 2 } { x + 2 } + \frac { - 5 } { x + 1 } + \frac { 2 } { ( x + 1 ) ^ { 2 } }\)
• C) \(\frac { - 2 } { x + 2 } + \frac { - 5 } { x + 1 } + \frac { - 2 } { ( x + 1 ) ^ { 2 } }\)
• D) \(\frac { 2 } { x + 2 } + \frac { - 5 } { x + 1 } + \frac { - 2 } { ( x + 1 ) ^ { 2 } }\)

---

Definitions:

Principal and Interest

The original amount of a loan (principal) combined with the cost of borrowing that money (interest).

Financial Covenants

Agreements between a borrower and lender setting specific financial ratios or milestones the borrower must maintain.

Minimum Financial Tests

Financial benchmarks or ratios a company must achieve or maintain to comply with certain agreements, often related to debt covenants.

Borrower Must

Obligations or conditions a borrower needs to fulfill as per the terms of the loan agreement.