$\"\"$

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The improper rational expression is $\"\"$ .

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The degree of numerator and the denominator of the expression are equal, hence first divide the numerator with the 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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$\"\"$ .

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Equate the coefficent of $\"\"$ , $\"\"$ and constants.

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

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

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

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$\"\"$

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$\"\"$

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Substitute the $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute the $\"\"$ and $\"\"$ in $\"\"$

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$\"\"$

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$\"\"$ .

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

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