Write the Form of the Partial Fraction Decomposition of the Rational

question 99

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression. It is not necessary to solve for the constants.
- $$\frac { 3 x + 4 } { ( x + 4 ) \left( x ^ { 2 } + x - 4 \right) ^ { 2 } }$$

• A) \(\frac { \mathrm { A } } { \mathrm { x } + 4 } + \frac { \mathrm { B } } { \mathrm { x } ^ { 2 } + \mathrm { x } - 4 } + \frac { \mathrm { Cx } + \mathrm { D } } { \left( \mathrm { x } ^ { 2 } + \mathrm { x } - 4 \right) ^ { 2 } }\)
• B) \(\frac { A } { x + 4 } + \frac { B x + C } { x ^ { 2 } + x - 4 } + \frac { D x + E } { \left( x ^ { 2 } + x - 4 \right) ^ { 2 } }\)
• C) \(\frac { \mathrm { A } } { \mathrm { x } + 4 } + \frac { \mathrm { Bx } + \mathrm { C } } { \mathrm { x } ^ { 2 } + \mathrm { x } - 4 }\)
• D) \(\frac { A } { x + 4 } + \frac { B } { x ^ { 2 } + x - 4 } + \frac { C } { \left( x ^ { 2 } + x - 4 \right) ^ { 2 } }\)

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Definitions:

Debt Financing

A method of raising capital through borrowing money from external sources, such as banks or bond investors, which needs to be repaid at a future date along with interest.