Precalculus 2014

 PAGE: 402 SET: Exercises PROBLEM: 1

The rational expression is .

Rewrite the expression using partial decomposition.

Find the values of and .

Multiple each side by the denominator fraction.

Equate the coefficent of  and constant.

and .

System of equations are and .

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

Find variable matrix .

.

Inverse of a matrix : .

.

The solution set is .

Therefore and .

Substitute the and  values in equation .

The partial decomposed function is

The partial decomposed function is .

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