Setting up partial fraction decompositions Give the

Chapter 4, Problem 26E

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QUESTION:

Setting up partial fraction decompositions Give the appropriate form of the partial fraction decomposition for the following functions.

\(\frac{2}{x\left(x^{2}-6 x+9\right)}\)

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QUESTION:

Setting up partial fraction decompositions Give the appropriate form of the partial fraction decomposition for the following functions.

\(\frac{2}{x\left(x^{2}-6 x+9\right)}\)

ANSWER:

Step 1 of 4

Proper fraction definition ; In a rational fraction  , if the degree of f(x) < the degree of g(x) , then the rational fraction is called a proper fraction.

         The sum of two proper fractions is a proper fraction.

                                  Example;

Partial fractions Depending upon the nature of factors of Denominator ;

1) When the denominator has non-repeated linear factors;

                             A non - repeated linear factor (x-a) of denominator corresponds a partial fraction of the form  , where A is a constant to be determined’

                 

      If g(x) = (x-a)(x-b)(x-c)............(x-n), then we assume that

                       =  ++ +...............+

Where A, B, C,............N are constants which can be determined by equating the numerator of L.H.Sto the numerator of R.H.S , and substituting x = a,b ,c ….n.

 

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