$\"\"$

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The rational expression is $\"\"$ .

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The degree of numerator is greater than the degree of the denominator of the expression,

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

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Multiple each side by the denominator fraction.

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$\"\"$

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$\"\"$

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Distuributive property :

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Equate the coefficent of the left side and right of the equation to obtain a system of two equation

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To solve the system in matrix form.

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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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$\"\"$

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

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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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$\"\"$

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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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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 $\"\"$ in $\"\"$ , $\"\"$ , $\"\"$ .

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$\"\"$

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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 fraction is

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$\"\"$ .

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$\"\"$

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The partial fraction is $\"\"$ .