Find the Partial Fraction Decomposition $$\frac { 9 x ^ { 2 } + 36 x + 8 } { ( x + 4 ) \left( x ^ { 2 } + 5 x + 6 \right) }$$

question 100

Multiple Choice

Find the partial fraction decomposition.
- $$\frac { 9 x ^ { 2 } + 36 x + 8 } { ( x + 4 ) \left( x ^ { 2 } + 5 x + 6 \right) }$$

• A) \(\frac { - 4 } { x + 4 } + \frac { 5 } { x + 1 } + \frac { - 4 } { x + 6 }\)
• B) \(\frac { - 4 } { x + 4 } + \frac { - 4 } { x + 1 } + \frac { 5 } { x + 6 }\)
• C) \(\frac { 4 } { x + 4 } + \frac { 5 x - 4 } { x ^ { 2 } + 5 x + 6 }\)
• D) \(\frac { 4 } { x + 4 } + \frac { - 4 x } { x ^ { 2 } + 5 x + 6 }\)

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Definitions:

Gold Foil

Thin sheets of gold used in scientific experiments, most famously in Rutherford's gold foil experiment which led to the discovery of the nucleus.

Sub-Atomic Particle

Particles smaller than atoms, including protons, neutrons, and electrons.

Atoms Produce Light

The phenomenon where atoms emit light when electrons jump from higher to lower energy levels, releasing photons.

Continuous Spectrum

A seamless spectrum of light (or other electromagnetic radiation) in which every wavelength within a certain range is represented.