Find the Partial Fraction Decomposition $u = e ^ { x }$

question 134

Multiple Choice

Find the partial fraction decomposition. [Hint: Use the substitution $u = e ^ { x }$ and recall that $\left. e ^ { 2 x } = \left( e ^ { x } \right) ^ { 2 } \cdot \right]$
- $\frac { - 8 e ^ { x } + 6 } { e ^ { 2 x } - 5 e ^ { x } - 6 }$

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

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Definitions:

Dualistic

Pertaining to a theory or concept that divides a subject into two opposed or contrasted aspects or entities.

Reflect on Self-Thought

The process of introspection, examining one's own thoughts, beliefs, and cognitive processes.

Post-Formal Cognitive

A stage of cognitive development that goes beyond Piaget's formal operational stage, characterized by the ability to deal with complex situations and understand that knowledge can be relative.

Self-Determination

The ability of an individual to make choices and govern their own life.