Write the Partial Fraction Decomposition of the Rational Expression $\frac { 3 x ^ { 2 } + 3 x + 18 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$

question 12

Multiple Choice

Write the partial fraction decomposition of the rational expression.​ $\frac { 3 x ^ { 2 } + 3 x + 18 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }$ ​

• A) \(\frac { 3 x + 3 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }\)
• B) \(\frac { 3 } { x ^ { 2 } + 6 } - \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }\)
• C) \(\frac { 3 } { x ^ { 2 } + 6 } + \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }\)
• D) \(\frac { 3 x + 18 } { x ^ { 2 } + 6 } + \frac { 3 x } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }\)
• E) \(\frac { 3 } { x ^ { 2 } + 6 } + \frac { 3 } { \left( x ^ { 2 } + 6 \right) ^ { 2 } }\)

---

Definitions:

Symbol Cu

The chemical symbol for Copper, a reddish-brown metal with high thermal and electrical conductivity.

Copper

A reddish-brown, malleable, ductile metallic element with high electrical and thermal conductivity, used in a variety of alloys and in electrical wiring.

Symbol Co

The symbol Co stands for cobalt, which is a chemical element with atomic number 27, known for its magnetic properties and used in alloys and batteries.

Cobalt

A chemical element with the symbol Co and atomic number 27, known for its metallic properties and use in alloys and battery production.