Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$$

question 314

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 26 x ^ { 2 } - 88 x + 76 } { ( x - 2 ) ( 2 x - 3 ) ^ { 2 } }$$

• A) \(\frac { 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { - 4 } { x - 2 }\)
• B) \(\frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 4 } { x - 2 }\)
• C) \(\frac { 5 } { 2 x - 3 } + \frac { - 5 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 4 } { x - 2 }\)
• D) \(\frac { - 4 } { ( 2 x - 3 ) ^ { 2 } } + \frac { 5 } { 2 x - 3 } + \frac { 5 } { x - 2 }\)

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Definitions:

Clumping

The aggregation or coming together of particles or cells, often observed in blood cells in response to certain conditions or agents.

Globulin

A type of protein in blood plasma that plays roles in immune response, blood clotting, and transporting substances.

Plasma Protein

Proteins found in blood plasma that perform various functions, including clotting, defence against pathogens, and transport of substances.

Immunity

The body's ability to resist or fight off infection, disease, or other unwanted biological invasion.