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:

Competitive Market

A market structure characterized by a large number of firms competing with each other to sell similar or identical goods and services.

Perfect Competition

A market structure with many buyers and sellers, where all firms sell identical products and no single buyer or seller can influence the market price.

Market Price

The current price at which a good or service can be bought or sold in a competitive marketplace.

Perfectly Competitive

Perfectly Competitive refers to a theoretical market structure characterized by a complete lack of economic friction, infinite buyers and sellers, and a perfectly homogeneous product.