Write the Form of the Partial Fraction Decomposition of the Rational

question 116

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.
- $$\frac { 3 x + 4 } { \left( x ^ { 2 } + x + 5 \right) ^ { 2 } }$$

• A) \(\frac { A x + B } { x ^ { 2 } + x + 5 } + \frac { C } { \left( x ^ { 2 } + x + 5 \right) ^ { 2 } }\)
• B) \(\frac { A x + B } { x ^ { 2 } + x + 5 } + \frac { C x + D } { \left( x ^ { 2 } + x + 5 \right) ^ { 2 } }\)
• C) \(\frac { \mathrm { A } } { \mathrm { x } ^ { 2 } + \mathrm { x } + 5 } + \frac { \mathrm { Bx } + \mathrm { C } } { \left( \mathrm { x } ^ { 2 } + \mathrm { x } + 5 \right) ^ { 2 } }\)
• D) \(\frac { A } { x ^ { 2 } + x + 5 } + \frac { B } { \left( x ^ { 2 } + x + 5 \right) ^ { 2 } }\)

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Definitions:

Appalachian Mountains

A major mountain range in eastern North America, extending from the Canadian Maritime provinces to central Alabama in the United States.

Thrust Faulting

A type of faulting caused by compressional forces where older layers of rock are pushed up and over younger layers.

Composite Volcanoes

Mountains formed from lava flows and pyroclastic eruptions, typically featuring steep profiles and periodic explosive eruptions.

Normal Faulting

A type of fault where the hanging wall moves downward relative to the footwall, typically occurring in regions undergoing extension.