Find the Partial Fraction Decomposition for the Rational Expression $\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$

question 201

Multiple Choice

Find the partial fraction decomposition for the rational expression.
$\frac { x ^ { 2 } } { x ^ { 2 } + 6 x + 9 }$

• A) \(1 + \frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }\)
• B) \(1 + \frac { 6 } { x + 3 } + \frac { - 9 } { ( x + 31 ) ^ { 2 } }\)
• C) \(\frac { 6 } { x + 3 } + \frac { - 6 } { ( x + 3 ) ^ { 2 } }\)
• D) \(\frac { - 6 } { x + 3 } + \frac { 9 } { ( x + 3 ) ^ { 2 } }\)

---

Definitions:

Honey

A sweet, viscous food substance produced by bees and some related insects from the floral nectar, known for its applications in cooking and medicinal properties.

Vegetarian

A dietary preference excluding meat and sometimes other animal products.

Conscious Effort

A deliberate and intentional attempt to perform an action or accomplish a goal.

Diet

The kinds of food that a person, animal, or community habitually eats, or a special course of food to which one restricts oneself, either to lose weight or for medical reasons.