Write the Partial Fraction Decomposition of the Rational Expression $$\frac { x ^ { 2 } + 3 x - 2 } { \left( x ^ { 2 } + 2 \right) ^ { 2 } }$$

question 66

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $$\frac { x ^ { 2 } + 3 x - 2 } { \left( x ^ { 2 } + 2 \right) ^ { 2 } }$$

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

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Definitions:

Hooke's Law

A principle stating that the force needed to extend or compress a spring by some distance scales linearly with respect to that distance.

Inversely

In an opposite or reverse manner, often referring to the relationship where as one variable increases, another decreases.

Fifth Power

A number or variable raised to the exponent of five, indicating it is multiplied by itself four times.

Hooke's Law

A principle stating that the force needed to extend or compress a spring by some distance is proportional to that distance.