Write the Partial Fraction Decomposition of the Rational Expression $\frac { 2 x ^ { 3 } + 4 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

question 120

Multiple Choice

Write the partial fraction decomposition of the rational expression.
- $\frac { 2 x ^ { 3 } + 4 x ^ { 2 } } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }$

• A) \(\frac { 2 x - 4 } { x ^ { 2 } + 5 } + \frac { - 10 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• B) \(\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { 10 x - 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• C) \(\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { 10 x + 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)
• D) \(\frac { 2 x + 4 } { x ^ { 2 } + 5 } + \frac { - 10 x - 20 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } }\)

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Definitions:

Cortex

The outermost layer of an organ or structure, such as the cerebral cortex of the brain, which is involved in numerous high-level functions including thought and action.

Medulla

The inner region of an organ or structure, such as the medulla oblongata in the brain or the adrenal medulla, involved in central functions.

Arcuate Artery

A type of artery, often referenced in relation to kidney or uterine structures, involved in supplying blood.

Ureters

Ureters are muscular tubes that transport urine from the kidneys to the bladder.