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

Tickets for the school play cost $6 for students and $9 for adults. On opening night, all 360 seats were filled, and the box office revenues were $2610. How many student and how

.1.Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67). ?Now le

A company makes and sells notebook computers. The company’s cost function in thousands of dollars is C(x) = 0.3x + 100, and the revenue function in thousands of dollars is R(x) = 0


Actually here we're not going to look at a general cubic polynomial.  Here we are jsut going to look at f ( x ) = x 3 . Really there isn't much to do here other than only plugging

so I''m having trouble. I honestly don''t under stand this. Y=4x+5. y=-1/4x+4 they want me to tell whether the line is parallel, perpendicular or neither I don''t know how.

Example Solve out the following system of equations. x 2 + y 2  = 10 2 x + y = 1 Solution In linear systems we had the alternative of using either method on any gi


Let a = 2 cm, b = 6 cm, and angle A = 60°.  How many solutions are there for angle B   We must calculate b sin A .  If it is less than a , there will be