Write the Partial Fraction Decomposition of the Rational Expression $\frac { 6 x ^ { 3 } + 4 x ^ { 2 } + 13 x + 15 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }$

question 98

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 6 x ^ { 3 } + 4 x ^ { 2 } + 13 x + 15 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }$

• A) \(\frac { x } { x ^ { 2 } + 3 } + \frac { 6 x + 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x + 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)
• B) \(\frac { x + 1 } { x ^ { 2 } + 3 } + \frac { 6 x + 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x + 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)
• C) \(\frac { 6 x - 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x - 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)
• D) \(\frac { 6 x + 4 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } } + \frac { - 5 x + 3 } { \left( x ^ { 2 } + 3 \right) ^ { 3 } }\)

---

Definitions:

Working Capital

The difference between a company's current assets and its current liabilities, indicating short-term financial health.

Discount Rate

The interest rate used to discount future cash flows to their present value, often utilized in determining an investment's worth.

Future Cash Inflow

Expected receipts of money to a business in the future, which can result from sales, investments, or financing.

Discount Rate

A specific rate used in the method of discounted cash flow analysis for calculating the present value of money flows anticipated in the future.