Write the Form of the Partial Fraction Decomposition of the Rational

question 9

Multiple Choice

Write the form of the partial fraction decomposition of the rational expression.Do not solve for the constants.​ $$\frac { x + 2 } { x ^ { 2 } ( 3 x - 8 ) ^ { 2 } }$$ ​

• A) \(\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } + 8 } + \frac { C } { 3 x - 8 } + \frac { D } { ( 3 x + 8 ) ^ { 2 } }\) ​
• B)​ \[\frac { A } { x - 2 } - \frac { B } { x ^ { 2 } } - \frac { C } { x ^ { 2 } ( 3 x - 8 ) } - \frac { D } { ( 3 x - 8 ) ^ { 2 } }\] ​
• C) \(\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } } + \frac { C } { ( 3 x - 8 ) ^ { 2 } }\) ​
• D) \[\frac { A } { x ^ { 2 } } + \frac { C } { ( 3 x - 8 ) ^ { 3 } } + \frac { D } { ( 3 x - 8 ) ^ { 3 } }\] ​
• E) \(\frac { A } { x } + \frac { B } { x ^ { 2 } } + \frac { C } { 3 x - 8 } + \frac { D } { ( 3 x - 8 ) ^ { 2 } }\)

---

Definitions:

Epidermis

The outermost layer of cells covering an organism, notably the skin of animals or the surface layer of plants.

Chloroplasts

Organelles found in plant and algal cells where photosynthesis occurs, converting light energy into chemical energy.

Photosynthesis

The process by which green plants and some other organisms use sunlight to synthesize foods with carbon dioxide and water, generating oxygen as a byproduct.

Opaque

Not allowing light to pass through; not transparent or translucent.