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

question 15

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) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$
- $$\frac { 7 x + 5 } { x ^ { 2 } - 8 x + 15 }$$

• 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) \(\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }\)
• -\[\frac { 7 x + 5 } { x ^ { 2 } - 8 x + 15 }\]
• A) \(\frac { A } { x - 3 } + \frac { B } { x - 5 }\)
• B) \(\frac { A } { x - 3 } + \frac { B } { x - 5 } + \frac { C } { x ^ { 2 } - 8 x + 15 }\)
• C) \(\frac { A } { x - 3 } + \frac { B } { x - 5 } + \frac { C x + D } { x ^ { 2 } - 8 x + 15 }\)
• D) \(\frac { A } { x - 3 } + \frac { B } { x - 5 } + \frac { C } { ( x - 3 ) ^ { 2 } ( x - 5 ) ^ { 2 } }\) Write the partial fraction decomposition of the rational expression.

Understand the concept of moral hazard and identify its occurrence in various contexts such as insurance and banking.

Comprehend the problem of adverse selection and its effects on markets, particularly in insurance and banking.

Recognize the role of government intervention in correcting market failures due to externalities and asymmetric information.

Analyze how policies can address global warming and pollution through market-based approaches like cap-and-trade systems.

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Definitions:

Organisational Upheaval

is a significant or sudden change within an organization that disrupts existing structures, practices, and relationships, requiring adaptation and realignment.

Crisis Management

The process by which an organization deals with major unexpected events that threaten to harm the organization, its stakeholders, or the general public.

Human Resource Conflict

Refers to disputes or disagreements between employees or between employees and management within an organization, often related to working conditions, policies, or interpersonal relationships.

Unplanned Change

Alterations in circumstances or conditions that occur without foresight or preparation, often requiring immediate adaptation.