Solution Found!
Setting up partial fraction decompositions Give the
Chapter 4, Problem 26E(choose chapter or problem)
Setting up partial fraction decompositions Give the appropriate form of the partial fraction decomposition for the following functions.
\(\frac{2}{x\left(x^{2}-6 x+9\right)}\)
Questions & Answers
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.