Partial fractions and partial fraction decomposition, Algebra

What we desire to do in this section is to begin with rational expressions & ask what simpler rational expressions did we add and/or subtract to obtain the original expression. The procedure of doing it is called partial fractions & the result is frequently called the partial fraction decomposition.

The procedure can be a little long and on occasion messy; however it is really fairly simple. We will begin by trying to find out the partial fraction decomposition of,

                                                           P ( x )/ Q ( x )

Where both P(x) & Q(x) are polynomials & the degree of P(x) is smaller than the degree of Q(x).   Partial fractions can just be done if the degree of the numerator is firmly less than the degree of the denominator. i.e. important to remember.

Hence, once we've determined which partial fractions can be performed we factor the denominator as wholly as possible. Then for each of the factor in the denominator we can utilize the following table to find out the term(s) we pick up in the partial fraction decomposition.

707_Partial fractions and partial fraction decomposition.png

Notice that the first & third cases are actually special cases of the second & fourth cases respectively if we consider k = 1 .  Also, it will entirely be possible to factor any polynomial down in product of linear factors ( ax+ b ) and quadratic factors ( ax2 + bx+ c ) some of which might be raised to a power.

Posted Date: 4/8/2013 3:02:56 AM | Location : United States







Related Discussions:- Partial fractions and partial fraction decomposition, Assignment Help, Ask Question on Partial fractions and partial fraction decomposition, Get Answer, Expert's Help, Partial fractions and partial fraction decomposition Discussions

Write discussion on Partial fractions and partial fraction decomposition
Your posts are moderated
Related Questions
30. 5x-1 greater than 29

Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?

The sum of the ages of Dorothy and Dona is 41. In 5 years, Dorothy will be twice as old as Dona. Find their age 3 years ago.

Compounded semiannually P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)^2 represents the valu


20

is (1,7),(2,7),(3,7),(5,7) a function