Write the Partial Fraction Decomposition of the Rational Expression $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

question 269

Multiple Choice

Write the partial fraction decomposition of the rational expression. $\frac { x ^ { 2 } } { x ^ { 4 } - 23 x ^ { 2 } - 50 }$

• A) \(\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 6 } - \frac { x ^ { 2 } } { 10 }\)
• B) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)\)
• C) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 ( x + 2 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)\)
• D) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)\)
• E) \(\frac { 1 } { 27 } \left( \frac { 2 } { x ^ { 2 } + 2 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)\).

---

Definitions:

Kilowatt-Hour

A unit of energy equivalent to one kilowatt of power expended for one hour of time, commonly used to measure electricity consumption.

Watts

The SI unit of power, indicative of the rate at which energy is transferred or converted.

Cell Phone Plan

A contract offered by telecom companies that includes a combination of voice, message, and data services for mobile phones.

Minutes

A unit of time equal to one-sixtieth of an hour, or 60 seconds.