Write the Partial Fraction Decomposition of the Rational Expression $$\frac { 4 x ^ { 2 } - 12 x - 48 } { x ( x - 4 ) ( x - 6 ) }$$

question 144

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { 4 x ^ { 2 } - 12 x - 48 } { x ( x - 4 ) ( x - 6 ) }$$

• A) \(\frac { x + 4 } { x ^ { 2 } - 4 } + \frac { 2 } { x - 6 }\)
• B) \(\frac { - 2 } { x } + \frac { 5 } { x - 4 } + \frac { 1 } { x - 6 }\)
• C) \(\frac { - 2 } { x } + \frac { 4 } { x - 4 } + \frac { 2 } { x - 6 }\)
• D) \(\frac { - 2 } { x } + \frac { 3 } { x - 4 } + \frac { 3 } { x - 6 }\)

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Definitions:

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The principle that states the ratio of voltage to frequency (V/F) should remain constant for AC drives to maintain torque.

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An electrical measurement expressing the potential difference between two points in a circuit, typically driving current flow.

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A type of electric motor that operates on the principle of electromagnetic induction, where the rotation of the motor is caused without direct electrical connection to the rotor.