Factor the Denominator of the Given Rational Expression, and Then $\frac { 11 x - 3 \sqrt { 3 } } { x ^ { 2 } - 3 }$

question 20

Multiple Choice

Factor the denominator of the given rational expression, and then find the partial fraction decomposition. $\frac { 11 x - 3 \sqrt { 3 } } { x ^ { 2 } - 3 }$

• A) \(\frac { 11 x } { x + \sqrt { 3 } } + \frac { - 3 \sqrt { 3 } } { x - \sqrt { 3 } }\)
• B) \(\frac { 4 } { x + \sqrt { 3 } } + \frac { 7 } { x - \sqrt { 3 } }\)
• C) \(\frac { 7 } { x + 3 } + \frac { 4 } { x - 3 }\)
• D) \(\frac { 7 } { x + \sqrt { 3 } } + \frac { - 4 } { x - \sqrt { 3 } }\)
• E) \(\frac { 7 } { x + \sqrt { 3 } } + \frac { 4 } { x - \sqrt { 3 } }\)

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Definitions:

Unemployment Rate

The unemployment rate is the percentage of the labor force that is jobless and actively seeking employment.

Natural Rate

The natural rate of unemployment is the level of unemployment consistent with a stable rate of inflation.

Inflationary Wage

Wage increases that match or exceed the rate of inflation, aimed at maintaining or increasing purchasing power over time.

Frictionally Unemployed

Individuals temporarily unemployed while transitioning between jobs, often viewed as a natural part of the labor market.