Find the Partial Fraction Decomposition for the Rational Expression $$\frac { - 2 x ^ { 2 } + 7 x + 24 } { ( x + 3 ) ^ { 2 } ( 3 x + 4 ) }$$

question 166

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { - 2 x ^ { 2 } + 7 x + 24 } { ( x + 3 ) ^ { 2 } ( 3 x + 4 ) }$$

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

Understand the basics of prenatal development stages and key terms related to it (zygote, embryo, fetal).

Recognize the impact of environmental influences and genetics on prenatal development and newborn traits.

Comprehend the significance of newborn reflexes and how they assist in survival and development.

Grasp the effects of teratogens, including alcohol and stress hormones, on prenatal development and child health.

---

Definitions:

Increasing Acidity

Increasing acidity refers to the phenomenon where the hydrogen ion (H+) concentration increases, making a solution more acidic.

Conjugate Base

The species formed after an acid donates a proton, characterized by its ability to accept a proton.

Stable

Referring to a chemical compound that does not easily decompose or change into other compounds under normal conditions.

HF

Commonly refers to hydrofluoric acid, a solution of hydrogen fluoride in water that is a highly corrosive acid.