$\"\"$

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The rational expression is $\"\"$ .

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Rewrite the expression using partial decomposition.

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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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Equate the coefficent of $\"\"$ and constant.

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

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$\"\"$

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System of equations are $\"\"$ and $\"\"$ .

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Write the system of equations into matrix form $\"\"$ , where $\"\"$ is coefficient matrix, $\"\"$ is variable matrix and $\"\"$ is constant matrix.

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$\"\"$

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Find variable matrix $\"\"$ .

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$\"\"$ .

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Inverse of a $\"\"$ matrix : $\"\"$ .

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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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The solution set is $\"\"$ .

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

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

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$\"\"$

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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 $\"\"$ .