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:

Nonretentive Outputs

Output signals or data in a control system that do not maintain their state after a power cycle or reset.

Latch Instruction

One-half of an instruction pair (the second instruction of the pair being the unlatch instruction) that emulates the latching action of a latching relay. The latch instruction for a programmable logic controller energizes a specified output point or internal coil until it is de-energized by a corresponding unlatch instruction.

MCR Zone

In programmable logic controllers (PLCs), a Master Control Relay zone, which refers to a section of the program controlled by a master relay for safety or operational purposes.