Find the Partial Fraction Decomposition $\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }$

question 53

Multiple Choice

Find the partial fraction decomposition.
- $\frac { - 31 x - 46 } { 2 x ^ { 2 } + 10 x + 8 }$

• A) \(- \frac { 5 } { 2 x - 2 } - \frac { 13 } { x - 4 }\)
• B) \(- \frac { 5 } { x + 2 } - \frac { 13 } { 2 x + 4 }\)
• C) \(\frac { 5 } { 2 x + 2 } + \frac { 13 } { x + 4 }\)
• D) \(- \frac { 5 } { 2 x + 2 } - \frac { 13 } { x + 4 }\)

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Definitions:

Carbon

A nonmetallic element that forms the basis of all known life on Earth, symbolized as C.

Oxygen

A chemical element with the symbol O and atomic number 8, essential for respiration in most life forms and used widely in industry.

Major Organic Product

The principal compound resulting from an organic chemical reaction, often the one present in the greatest amount or yield.

Reaction

An operation in which different substances amalgamate, producing new variants with altered traits.