Find the Partial Fraction Decomposition $$\frac { - 7 } { x ( 3 x - 1 ) ( x + 1 ) } = \frac { A } { x } + \frac { B } { 3 x - 1 } + \frac { C } { x + 1 }$$

question 315

Multiple Choice

Find the partial fraction decomposition.
- $$\frac { - 7 } { x ( 3 x - 1 ) ( x + 1 ) } = \frac { A } { x } + \frac { B } { 3 x - 1 } + \frac { C } { x + 1 }$$

• A) \(\mathrm { A } = - 7 , \mathrm {~B} = \frac { 63 } { 4 } , \mathrm { C } = \frac { 7 } { 4 }\)
• B) \(\mathrm { A } = 7 , \mathrm {~B} = \frac { 63 } { 4 } , \mathrm { C } = \frac { 7 } { 4 }\)
• C) \(\mathrm { A } = 7 , \mathrm {~B} = - \frac { 63 } { 4 } , \mathrm { C } = - \frac { 7 } { 4 }\)
• D) \(A = - 7 , B = - \frac { 63 } { 4 } , C = - \frac { 7 } { 4 }\)

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Definitions:

Undesirable Behavior

Actions or reactions that are not wanted or considered negative in a particular context.

Unpleasant Consequence

A negative outcome or punishment that follows an undesired behavior, used to decrease the likelihood of that behavior occurring again in the future.

Aversion Therapy

A form of psychological treatment where undesirable behaviors are paired with unpleasant stimuli to reduce the behavior.

Nail-Biting

A common oral compulsive habit or behavior often associated with anxiety or stress.