Find the Partial Fraction Decomposition for the Rational Expression $$\frac { 10 x ^ { 2 } - 124 x + 12 } { \left( x ^ { 2 } + 2 x - 6 \right) ( x - 10 ) }$$

question 170

Multiple Choice

Find the partial fraction decomposition for the rational expression.
- $$\frac { 10 x ^ { 2 } - 124 x + 12 } { \left( x ^ { 2 } + 2 x - 6 \right) ( x - 10 ) }$$

• A) \(\frac { 12 x } { x ^ { 2 } + 2 x - 6 } + \frac { 2 } { x - 10 }\)
• B) \(\frac { 12 x } { x ^ { 2 } + 2 x - 6 } + \frac { - 2 } { x - 10 }\)
• C) \(\frac { 2 x } { x ^ { 2 } + 2 x - 6 } + \frac { - 12 } { x - 10 }\)
• D) \(\frac { 12 x } { x - 10 } + \frac { - 2 } { x ^ { 2 } + 2 x - 6 }\)

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Definitions:

Real Number Line

A line that represents all possible real numbers, including rational and irrational numbers, in a continuous line where each point corresponds to a unique real number.

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Pounds Per Square Inch

A unit of pressure represented as psi, indicating the amount of force exerted per square inch of area.

Inequality

A mathematical statement indicating that two expressions are not equal, using symbols such as <, >, ≤, or ≥.