Find the Partial Fraction Decomposition for the Rational Expression $\frac { 8 x ^ { 2 } - 97 x + 18 } { \left( x ^ { 2 } + 3 x - 6 \right) ( x - 8 ) }$

question 328

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { 8 x ^ { 2 } - 97 x + 18 } { \left( x ^ { 2 } + 3 x - 6 \right) ( x - 8 ) }$

• A) \(\frac { 11 x } { x ^ { 2 } + 3 x - 6 } + \frac { - 3 } { x - 8 }\)
• B) \(\frac { 11 x } { x ^ { 2 } + 3 x - 6 } + \frac { 3 } { x - 8 }\)
• C) \(\frac { 11 x } { x - 8 } + \frac { - 3 } { x ^ { 2 } + 3 x - 6 }\)
• D) \(\frac { 3 x } { x ^ { 2 } + 3 x - 6 } + \frac { - 11 } { x - 8 }\)

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Definitions:

Flatus

Gas generated in the stomach or intestines that can be expelled through the rectum.

Ileum

The third and final part of the small intestine, which plays a critical role in absorbing nutrients and water.

Stoma

A surgically created opening on the surface of the body that connects an internal organ to the external environment.

Colostomy

A surgical procedure that creates an opening (stoma) from the colon to the abdominal surface to allow for the diversion of fecal matter.