Write the Partial Fraction Decomposition of the Rational Expression $$\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$$

question 7

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$$

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

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Definitions:

22 Ω

A unit of electrical resistance indicating that an object has a resistance of twenty-two ohms.

60 V

A potential difference of sixty volts between two points in an electrical circuit.

Total Resistance

The overall opposition to current flow in a circuit, often calculated by summing individual resistances in series and applying specific formulas for parallel components.

Parallel Circuit

An electrical circuit in which components are connected across common points, allowing multiple pathways for current to flow.