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

question 167

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) $\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }$
- $\frac { 3 x ^ { 2 } - x - 8 } { x ( x + 1 ) ( x - 1 ) }$

• 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) \(\frac { A } { x + 6 } + \frac { B } { x + 2 } + \frac { C } { ( x + 6 ) ^ { 2 } ( x + 2 ) ^ { 2 } }\)
• -\(\frac { 3 x ^ { 2 } - x - 8 } { x ( x + 1 ) ( x - 1 ) }\)
• A) \(\frac { 8 } { x } + \frac { - 2 } { x + 1 } + \frac { - 3 } { x - 1 }\)
• B) \(\frac { 8 } { x } + \frac { 2 } { x + 1 } + \frac { - 3 } { x - 1 }\)
• C) \(\frac { 8 } { x } + \frac { - 2 } { x + 1 } + \frac { 3 } { x - 1 }\)
• D) \(\frac { 8 } { x } + \frac { - 3 } { x + 1 } + \frac { 2 } { x - 1 }\)

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Definitions:

Genetic Drift

A mechanism of evolution that involves random changes in the frequency of alleles within a population over time.

Body Build

The physical composition of an individual, including their muscle, bone, and fat distribution, which can influence their physical capabilities and appearance.

Extremities

The furthest points or limits of something; can also refer to limbs of the body, such as hands and feet.

Macroevolution

Large-scale evolutionary changes that occur over geological time, leading to the emergence of new species and broader taxonomic categories.