$\"\"$

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The partial fraction of decomposition rational expression is $\"\"$ .

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The degree of the numerator is greater than that of the denominator, hence divide the numerator by denominator.

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$\"\"$

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The expression can be written as $\"\"$ .

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Rewrite the expression into partial fraction

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$\"\"$

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Find the values of $\"\"$ and $\"\"$ .

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Multiple each side by the denominator fraction.

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$ .

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Equate the coefficient of $\"\"$ and constants.

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$ .

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Substistute the $\"\"$ and $\"\"$ values in equation $\"\"$ .

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$\"\"$

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The partial decomposed function is $\"\"$ .

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$\"\"$

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Graph :

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Graph the functions $\"\"$ and $\"\"$ .

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$\"\"$

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Observe the graph

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$\"\"$

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$\"\"$

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The partial decomposed function is $\"\"$ .