Write the Partial Fraction Decomposition of the Rational Expression $$\frac { x ^ { 2 } } { x ^ { 4 } - 21 x ^ { 2 } - 100 }$$

question 34

Multiple Choice

Write the partial fraction decomposition of the rational expression.
$$\frac { x ^ { 2 } } { x ^ { 4 } - 21 x ^ { 2 } - 100 }$$

• A) \(\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } + \frac { 5 } { 2 ( x - 5 ) } - \frac { 5 } { 2 ( x + 5 ) } \right)\)
• B) \(\frac { 1 } { x ^ { 2 } } - \frac { 1 } { 2 } - \frac { x ^ { 2 } } { 20 }\)
• C) \(\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } + \frac { 5 ( x + 4 ) } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x - 5 ) } \right)\)
• D) \(\frac { 1 } { 29 } \left( \frac { 4 } { x ^ { 2 } + 4 } - \frac { 5 } { 2 ( x - 5 ) } + \frac { 5 } { 2 ( x + 5 ) } \right)\)
• E) \(\frac { 1 } { 29 } \left( \frac { 1 } { x ^ { 2 } + 4 } + \frac { 1 } { 2 ( x - 5 ) } - \frac { 1 } { 2 ( x + 5 ) } \right)\)

---

Definitions:

Premises

Statements or propositions that provide the basis for a conclusion in an argument.

Major Premise

The first statement in a syllogism that contains the major term and provides a general principle or rule.

Middle Term

In a syllogism, the term that appears in both premises but not in the conclusion, used to connect the other two terms of the argument.

Major Term

Refers to the predicate of the conclusion in a categorical syllogism, which is a key component in deductive reasoning.