$\"\"$

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

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Rewrite the expression as partial fraction with constant numerators, $\"\"$ , $\"\"$ $\"\"$ and $\"\"$ and denominators that are linear factor of the orginal denominator.

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