Decompose P/Q, Where Q Has Only Distinct Linear Factors
Write $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$

question 177

Multiple Choice

Decompose P/Q, Where Q Has Only Distinct Linear Factors
Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the
constants.
1) $\frac { 6 x - 4 } { ( x + 6 ) ( x + 2 ) }$
A) $\frac { A } { x + 6 } + \frac { B } { x + 2 }$
B) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }$
C) $\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }$
D) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$
- $$\frac { x } { x ^ { 2 } + 5 x + 6 }$$

• A) \(\frac { A } { x + 6 } + \frac { B } { x + 2 }\)
• B) \(\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ( x + 2 ) }\)
• C) \(\frac { \mathrm { A } } { x + 6 } + \frac { \mathrm { B } } { \mathrm { x } + 2 } + \frac { \mathrm { Cx } + \mathrm { D } } { ( \mathrm { x } + 6 ) ( \mathrm { x } + 2 ) }\)
• D) \(\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }\)
• -\[\frac { x } { x ^ { 2 } + 5 x + 6 }\]
• A) \(\frac { 3 } { x + 3 } + \frac { - 2 } { x + 2 }\)
• B) \(\frac { - 3 } { x + 3 } + \frac { 2 } { x + 2 }\)
• C) \(\frac { 2 } { x + 3 } + \frac { - 3 } { x + 2 }\)
• D) \(\frac { 3 } { x + 3 } + \frac { 2 } { x + 2 }\)

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Definitions:

Nerves

Bundled axons that form neural “cables” connecting the central nervous system with muscles, glands, and sense organs.

Action Potentials

Electrical impulses that neurons generate to transmit information through the neuron's axon to another neuron or to a muscle or gland cell.

Synapses

The junctions between two neurons, where the transfer of electrical or chemical signals occurs.

Interneurons

Neurons that transmit impulses between other neurons, especially as part of reflex arcs and neural networks within the central nervous system.