Write the Partial Fraction Decomposition of the Rational Expression $\frac { x + 1 } { x ^ { 2 } - 2 x - 8 }$

question 41

Multiple Choice

Write the partial fraction decomposition of the rational expression.Check your result algebraically.​ $\frac { x + 1 } { x ^ { 2 } - 2 x - 8 }$ ​

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

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Definitions:

Opportunity Cost of Capital

The potential return lost by investing capital in one project instead of another with a higher return.

Expected NPV

The anticipated net present value, which estimates the present value of future cash flows minus initial investments, accounting for risk and uncertainty.

Project

A scheduled collection of connected activities designed to be completed within a specific timeframe and under predetermined budget and restrictions.

Discount Rate

The interest rate used to determine the present value of future cash flows in discounted cash flow analysis.